How soon should rehab n strengthening exercises start after a 2nd grade ankle sprain? should i wait till there's totally no more pain when walking?

3-4 weeks: Typically it takes 3-4 weeks for ligaments to heal. Starting physical therapy around that time may assist with balance, proprioceptiom, and strengthening. You'll still have residual swelling for a while so don't wait until there is no pain. However if pain continues to increase, you might need to get reevaluated for a possible pathologies(olt) that can happen with severe to moderate sprains.