I had ligament damage in my ankle about 3 months ago and now when ever i play sports, it swells up like it did when i injured it and is painful. why?

Incomplete healing: It sounds like your ankle has not fully healed. After the injury you describes, it can take weeks or months to fully heal. You should consider rest, range of motion exercises, and splinting - especially during activities that require side-to-side motion. If these do not work, formal consultation with an orthopedist or physical therapist may be helpful. Remember: you have a high risk of re-injury!