It would depend upon the mechanism and extent of the shoulder injury. Was it a glenohumeral dislocation?
A Hill Sachs Deformity typically (but not always) occurs during a dislocation.
This is what causes long term "instability of the shoulder" and is typically a DQ, because it increases the odds of another dislocation in the future.
If in fact your doctor can say that you have 100% range of movement and there is no significant difference in strength from one shoulder to the other, then maybe it will be okay.
No one can tell you what the outlook is. You should just get that letter from the Orthopod, and hope for the best.
The Air Force could move ahead with granting a scholarship, or not. It all depends upon the extent of your recovery and the needs of the Air Force, at that time.