My lower back is making me feel painful all the time. Is there a way to cure this. Will playing badminton and going for diving make it worst?

Diving with bad back. I don't recommend diving if you are already in pain. If you haven't already been evaluated by your physician, recommend that. You can discuss the option of acupuncture with your doctor as an adjunct. The time to dive is after your back issues have been addressed & have improved. Take cafe.
Exercise. You should first figure out why you are having constant back pain. Most of us experience back pain during our lifetime. Fortunately, it usually lasts less than 6 weeks. Performing a good exercise program (core stabilization exercises), aerobic conditioning, proper nutrition and proper sleep all help. If you have any concerns, please see a physician. Otherwise, go enjoy the activities you like.