I was doing ABBH I, so I was doing chin-ups, bent over BB rows, bench, and dips for upperbody. I had been doing dips for three weeks and was doing a warmup set with bodyweight when my injury happened. It's definitely not the teres minor, because it feels more like this tendon connects to the lower shoulder/top of bicep rather than to the rotator cuff.
Since I can't work horizontal chest I'll probably just end up doing back/legs/shoulders until this feels 100%.
I'm not sure about the 1 handed-press deal; I'm sure there's CNS improvement to the other arm, but I'd rather not risk a muscle imbalance.