My gums ache when resting after vigorous activities ?

Clenching: You may be clenching your jaw/teeth during the vigorous activity. Try using a mouth guard or consult your dentist for a custom appliance.

Possibly TMJ: Possibly you are clenching your jaws during work outs or vigorous activity. That would lead to jaw and possibly tooth or gum pain. I would suggest seeing your dentist or oral surgeon. Another possibility would be a hairline fracture in one of your teeth or tooth roots. Less likely would be some type of nutritional deficiency.