Update on Training: so, I've been fighting this nasty case of shin splints since forever. I have stopped running (except for a 3mile PFT run I did once, about a month ago), and assumed that the splints would be gone.
So, as written above, I went for a 1 mile light jog on the treadmill. The next day, I felt the splints. Worse yet, if I pressed on the shins, I could feel one small point of pain in particular. This is an indication of a stress fracture.
Since I haven't been running, I was dumbfounded as to how my splints could have progressed to a fracture.
Turns out, none of my doctors/physical therapists told me to stop lifting heavy weight. And all that extra load-bearing on the tibia from heavy squats and deadlifts (I am a relative newcomer to lifting) could be contributing to the issue.
That being said, maybe I'm just feeling phantom pain. Or maybe it is just shin splints.
In any case, I dug deeper than I ever before about medial tibial stress syndrome, stress fractures, compartment syndrome, and shin splints. I discovered what could be another problem: anterior pelvic tilt. In other words, my posture is bad.
In this case, my posture is bad because I have A) weak deep-core strength, B) tight quads, hip-flexors, and low-back, and C) weak hamstrings and glutes.
So, my program at the moment includes extra strengthening of the shitty muscles, lots of stretching of the tight muscles, and more deep-core work both during and after my lifts. In the mean time, I will continue to ice, compress, and elevate my lower legs.
It remains to be seen if I have progressed to a stress fracture, or if I have just been treating my shin splints with the wrong solution.