Sounds like overuse, but hard to diagnose of course... different kind of pain IME than the one that comes from working *at* the limit but not above it.

So, see a doctor, don't do stuff that hurts. Maybe try careful isometrics and gentle stretching (where the maximum of pain should be the "release from tension" kind) not only in the gym, but also at the laptop. I found pulse warmers a good thing when working at the computer...

I'm trying to do my pushups on a bar because of shoulder issues. It's hard enough, no need to make it painful...