I too am rehabbing from surgery -- rotator cuff. I on the other hand was told I should walk as soon as possible and run only after a week. It took me 10 days to hit a full run. I was able to continue core and lower body workouts and upper body as long as it did not involve lifting, especially over my head.
Able being a key word. Everything I was doing was uncomfortable so I was not willing to workout. So I hired a trainer. He is doing PT ahead of the doctor's green light. Just stretching that fits into what I have been allowed plus weights. I am doing whatever he tells me up to no pain. I feel like such an old man, not able to handle 10 pounds.
Oh, back to you. Since you have a therapist, ask this question to him/her. That is where you should find your real guidance.
The key is not to rush things beyond your capability. The goal is rebuilding.
Start by doing what is necessary, then do what is possible and suddenly you will be doing the impossible -- St Francis of Assisi
Rock 'n' Roll Dublin Half Marathon, Dublin, Ireland, 8/5/2013 ie.competitor.com/dublin/