I decided to get it checked out by my local specialist. There's a doctor very close by that did my ingrown toenail surgeries in the past. He's a foot and ankle specialist, so I figured I'd suck it up and pay the specialist copay (I'm poor lately, and 50 bucks is a lot of money to me) to see him and be extra sure that things heal up right (originally went to my regular doctor). He prodded and bent my ankle around to find where it hurt and took an x-ray. Gave me some anti-inflammatory meds and told me that the injury was where the bone of the heel meets with the tendon. So it's definitely tendonitis like my PCP had told me. According to the specialist, though, since the injury is at the very base of the heel I should actually be stretching the crap out of it. He said the story would be different if I had bursitis or achilles tendonitis higher up on the tendon, but with the location of the pain the best thing to do is stretch like crazy to force the muscles in the calves to lengthen.
tl;dr version: It's feeling pretty good, and I'm surprised at how quickly I've been able to get back to walking comfortably since I started stretching it harder.