Hope you are doing good in this pandemic situation. Let me get straight to the point and tell you that medical and Dental counselling of each state is independent of every other state.  Two States may or may not have similar counselling procedure. But for Karnataka and Tamilnadu let me tell you that you cannot use a caste certificate from other state should have been issued from the current state only. Also there is a category change in your case therefore I would advise you to get a new certificate concerning your cast e immediately.

Also you should definitely use our college predictor tool to know about your best chances in medical colleges all over India don't just  limit yourself to a single region.