I did end up taking a few weeks off from pottery (throwing anyway).
My shoulder stopped aching. Last week, while working in the garden, I pulled something out of the ground wrong and that night, boom, shoulder pain.
Today, after pottery class.... boom, shoulder pain. With pottery, I notice it mostly when I'm centering anything larger than 4 lbs.
I'm quite aware of ergonomics at the PC. My monitor is sitting on a monitor riser at the right height and my keyboard and mouse are also at good positions. I've been in situations where they've not been good and have suffered. This is certainly not the same.
So, yes, I'm using Dr. Google to diagnose, but I do also have a friend at an orthopedist's office. When I told her about it (before even mentioning being a potter), she said, "sounds like tendonitis to me. Do you do this a lot" and she put her hands in a position as if she were picking something up. ... basically, a potting position. "Yup, I throw pottery on the wheel."
Bottom line, I'm 39 years old and my body is not what it used to be. I need to come to terms with the fact that I'm middle aged and need to start treating injuries properly!