I've got the same issue in my right shoulder; previously diagnosed as bicep tendonitis at the proximal insertion. Developed it before SS while doing P90.
These days, it flares up and then recedes. Some mornings in the past, I couldn't raise my arm. Bench press aggravates it. Chins help.
The first time, I beat it with naproxen. Were you prescribed any?
If it's really a tendon issue, and that's not uncommon, NSAIDs are the typical recommendation around here. You've got to alleviate the inflammation. Do a search for the ibuprofen protocol.