I ran with Lydia for a few "personal quests" in and around Whiterun during my first playthrough. I was doing mostly hunting and gathering and came across a giant camp. Keep in mind that this was my first playthrough. I knew nothing about Skyrim, save what I had learned while getting from Helgen, through Riverwood, and to Whiterun. I was, of course, instantly spotted by the giant and his mammoth, since I had managed to wander right into his camp and found myself next to his chest, so he and his beast went aggro on me. The first thing Lydia did was to jump into the thick of things and take on the giant, single-handed, while I was backpedaling to get a safe place for sniping with my bow. That was the point at which I realized that Bethesda had not improved followers from Oblivion. Lydia died, I hightailed it out of Dodge, and never looked back on followers in Skyrim, again.
To be fair, I've let a couple follow me around a bit, but I find them much more useful as cannon fodder than as allies. I play stealth-based characters. I expect to be seen. When that happens, I retreat into the shadows and become unseen, again. Followers will instantly blow your cover and any chance you have of regaining any stealth advantage. I hated them in Oblivion, with but a few notable exceptions, and I hate them even more in Skyrim.
Anyway, Lord Garon has a problem. I'll try to address his issues.
I've been playing on Adept level since day one. This is my eighth playthrough and I've beaten the Main Quest once. I've beaten all the primary questlines (Thieves Guild, Dark Brotherhood, Bard's College, College of Winterhold) at least twice. I've beaten all the Daedric quests at least once. I've beaten most of the quests centering around the hold capitols at least three times. I'm really not having the problem staying alive that you are, and I honestly don't know why you're having that problem.
Let me tell you about my basic build.
I play a Khajiit. Why? Well, I thought they were cute in Oblivion (they really were) and figured they would be in Skyrim. I was wrong, but they have some perks, that fit right into my playstyle as a stealth specialist. I also like that their unarmed attack (15 points of damage) outclasses any weapon you'll find until you can start finding stuff better than iron and you can improve it at the smithing stations. Frankly, I don't really think that, in the long run, your character's race makes much difference. I just like the Khajiit because of some very early advantages, especially when coupled with Thief's Stone benefits.
You have to have a range attack in this game, and it has to be an effective one. As a pure melee warrior you're going to Hell in a handbasket. You'll encounter enemies who can take you out from a distance. That's just the way the game is designed. I generally play around an archer-battlemage build. I'll experiment a bit with that from one playthrough to another, but my M.O. is take out my enemies from afar, or at least weaken them enough to make it easy to kill them in melee. A combination of bow and destruction magic works ideally in this game.
I use light armor -- exclusively. In fact, I never wear anything but leather until very late in the game, when I've improved my Smithing skill to the point at which I can make dragonscale armor. This means I do whatever I need to do to create a full set of leather armor while I'm still in Riverwood. If that means doing a bit of hunting to get pelts, then I do it, although if I have enough money I'll just buy the leather I need.
While I'm at it, I grind my Smithing just high enough to start making and improving steel armor and weapons. Then I make myself a steel sword and improve it. I improve my leather armor. It won't be much of an improvement, but at early levels even a few points can make all the difference in the world.
Once I have a steel sword (I've experimented with ordinary sword and shield, and I prefer greatswords in this game) and my leather armor, I'm ready to tackle real enemies -- i.e., I head to Bleak Falls Barrow. Most of your opponents at this point have, at best, iron weapons and fur armor, neither improved (of course). This gives you a decided advantage early in the game. Keep your Smithing skill high enough to maintain this edge, and improve your gear whenever you get a chance. This is a game in which a minute advantage can mean the difference between winning and losing a battle.
Don't forget magic, even if you're going to play a warrior character. Casting Muffle or Oakskin before getting involved in a fight can give you a decided edge. You can whittle down an enemy mage's Magicka with Sparks (which you can get off the mage's corpse in Helgen on your way out). Frostbite can slow an advancing enemy down while you're backpedaling. Just about everything takes DOT (damage over time) from Flames. And like your gear, don't forget to upgrade your spells whenever you get a chance. Remember, you can buy spells from the Riverwood Trader. Do it at your earliest opportunity.
Stats: I try to stay balanced. I generally let Health trail Magicka by ten points early in the game. I'll let Stamina trail Health by the same amount. Later on the game I'll up those values to 20, maybe even 30. I'm not primarily a melee fighter, and two-handed power attacks take a lot of Stamina. I use that greatsword for finishing off an opponent -- not for the main battle. With improved armor I can afford to concentrate a bit more on Magicka than on Health.
Perks: I honestly don't use most of them. I put points into basic Stealth, One-Handed, Archery, Destruction, and Smithing early on. I'll try to get the damage bonus perks out of the Stealth tree. Most of the rest of it is fluff that can wait until later in the game. I seldom put any points into One-Handed beyond the basic one. I'll fill out the Archery tree up to getting critical hit bonuses and Eagle Eye. Again, the rest is fluff. Save it for later. I'll pour a lot of points into Destruction. Keep up-to-date on the main branch (Novice - Apprentice - Adept, etc.), but don't forget to buff your basic elemental magic. I never bother with the higher nodes on those three branches. You want Dual-Casting as soon as you can get it. Stun-locking a tough opponent can make a fatal encounter easy to overcome.
Alchemy: Don't grind it. Just use it as you move along in the game. I look for the ingredients I know will make potions that I use. I like poisons -- Slow and Paralysis poisons can give you an overwhelming edge at any level of the game, especially if you combine those effects with Lingering Damage Health and Damage Health. I make potions that boost my Stealth and Archery skills, and give my Invisibility. Make random potions out of all your other ingredients and sell them for a good profit.
Enchanting: This is a must-have, but one that you can put off until later in the game. Don't waste points in Enchanting perks until you're well-along and have gotten your basic survival skills buffed out. Then start grinding that tree up to and including Dual-Enchanting. Frankly, at that point in the game you can create weapons and armor which far-outstrip anything your opponents can have.
You'll probably find your first enchanted weapon (a bow) at the top-most tower of Valtheim Towers. It's leveled, but an enchanted bow at the earliest point in the game can give you a real advantage over just about everything. Clear this area at your earliest opportunity, even before you get a mission to kill the bandit leader, there. Save your game before you exit Whiterun to go there, though. I'm not sure how the game handles this, but it's possible that the exact bow is determined upon cell loading, and I'm not sure where that cell begins. You can get some junk (like bows that make your opponents flee -- they're dead, what's the use in that?). You might have to try several times before you get a good one (elemental damage -- any type). Get it before you take on the main quest. It'll help you with your first dragon fight.
I could go on-and-on, but I think this is enough for starters. The key, I think, to winning in this game is to stay just one step ahead of your opposition in terms of the gear you have and the spells you know. And, as Melka, the friendly hagraven in "The Affairs of Hagravens" says: "Careful here. There's a trick to this. The trick is to not bleed to death! Ah, there's a lever, too." In other words, you have to use every single tool at your disposal -- and that includes your brains. Try to hack and slash your way through Skyrim and you'll probably wind up bleeding to death.