If you're wary of medication, and at your age the risks certainly are higher than with someone older, exercise and therapy are valid treatment options for mild or moderate depression. The exercise should be a very structured plan though, just as you would take a pill on a daily basis, you would want to get something written down and take each exercise session "as prescribed" so to speak.

It's worth seeing your doctor perhaps once more if you're willing to and explain that you're not avoiding treatment you just want to try a different treatment, see if she's willing to help you get set up with a therapist or an exercise program. if not you deserve better care. Good luck!