Pain at r ligament of l ankle 11 weeks after sprain. 1 doc said ligament injury, wear brace n rest to heal. 1 doc said ankle exercise. who's right?

Depends : On how severe the sprain was. Is there instability after injury. Any ligament tears. If bad sprain with ligament damage it can take 4 mos. If pain but no swelling than can start physical therapy. If pain is too severe you may need MRI to rule out bone bruise or fracture.

Both: Depending on the severity, immobility is the first step. Gentle range of motion should be started early and then progress as tolerated to include strengthening. I would put more weight on a specialist if you went to see one. You should call them and ask this question.

Sprain: As stated , it depends on the severity . Actually both opinions you have are correct. Start with conservative care , then progress to rehab like work. At 11 weeks it is probably time for some imaging studies to see what is going on with the damage.