Hey kaoshin, didn't you say you are 13?
Ideally, you should do resistance training with bodyweight only. You can do push-ups, dips, pull ups with various grips, squats, lunges, swimming, sprints and make some good fundamental strength gains. More importantly, you will have dynamic strength - the ability to apply force while moving, which is important for martial arts.
How do you make the most of these workouts? Increase the number of sets, change the speed or angle.
Seeing that you are a very determined young guy and will probably want to lift weights anyway
, I'd recommend that you keep your weight training in the 15-20 rep range for awhile before you hop into the 12-15 rep range. At your age, you really shouldn't go lower than the 12-15 rep range and that is strictly my opinion.
Talk to your doctor and see what he says.