Left Knee pain. The treatment for it?

I am a lefty 27 years,173cm, 75kgs. I met with an accident 1.5 year ago to my left knee with which I got left knee pain. Doctor advised me to take x Ray but nothing found in it at that time. Now again I'm feeling pain in my left knee when I play badminton or tt or running for longer time more than 45min. When I am slightly try to move my knee cap I am sensing a movement in my left knee cap. There is no movement in the right one. I don't have any pain while walking n running or bending ... but I am feeling the pain only after playing for more than 45min or so I am still able to play with pain but I am left knee feels exhausted n little pain What problem I am having ? How to detect what tests I have to do ? What's the treatment for it ?