Question - Shoulder Dislocation (gunslinger immobilization)

This upcoming Sunday will be six weeks since my shoulder dislocation. I am a baseball player and dislocated my non-throwing shoulder. The shoulder was dislocated sliding back into a base and another player steped on my shoulder. I have been prescribed a gunslinger immobilizer.

What is confusing to me is that my doctor told me 4 months before I can swing or play. However, my therapist said it only takes 12 weeks for ligaments to heal. So why can't I come back after 12 weeks instead of 4 months.

Next question is that when six weeks arrives, I will be taking my immobilizer off. The doctor said I can start weight lifting again as long as I avoid overhead lifts and bench press. So with this I was wondering if I can squat. I was wondering if the weight on the back of the shoulder would be bad.

Finally,

Can I do sprints?

Jog?

Agilities?

Thank you for helping me and look forward to a response.