OK, so before I went messing around with ENB stuff, I decided to go ahead and check the issue 1 more time. So, it seems I was mistaken about the effect happening on more than my character's skin. When I moved the camera to the side, it appears that it was just the glow and not the weird effect. Here's a couple of screenshots.
The effect also happens on NPCs. Here it is on the Angel follower.
I didn't notice the effect on anything else. Also, I installed Particle Patch for ENB, but it didn't help.