Possible injury around right shoulder/tricep

Hello, I am 41 male at 290lbs. I have been on and off working out for a few years, however this year I have been alot more commited on losing the weight and gaining strength. I have been doing a 3 day full body workout, however about 3 weeks ago I notice that I know have a slight pain, tightness in my upper arm, around the tricep/shoulder area.

I really only feel it when I am doing a press motion like a bench press and lat raises. I still can move some weight but I have had to move the weight down. I have an appointment coming up to have it looked up but I'm sure I pulled the muscle since I do still have full motion of my shoulder just a slight pain when I open my arms wide.

I'm sure it's going to be some rest or maybe some PT the Dr might give me, if so should I focus on just cadio at the gym or should I still press on and go lighter on my workouts to help prevent muscle loss while it recovers. Never had really a injury before like this.