Hi there! First, bleeding gums and soreness could be due to clenching your teeth and grinding your teeth during exercise. It could also be an indication of vitamin deficiency, especially vitamin C. If you have changed your diet to whole foods and reduced the caloric intake you might indeed be deficient in vitamins. Especially those that are require fat to be absorbed. Increased bleeding/sensitivity also can be related to hormonal factors, such as TOM for example or pregnancy (NO, I'm not saying you are pregnant - just giving an example!)
Canker sores are another issue -- usually these are a result of an autoimmune process, whereby your body removes the surface layer of tissue. They are really, really painful (got them too!). As for cause, no one really knows for sure. Stress is often considered as one factor; vitamin deficiency is another; hormonal factors may be another (TOM, for example). I've had people absolutely swear that increasing vitamin C intake heals them and prevents them, while others say that increasing vitamin C makes them worse. Others swear by multivitamins. What I do is take a maternity-grade multivitamin and up my vitamin C. You might consider increasing your fat intake to ensure that those fat-dependent vitamins are actually absorbed.
In the mean time, go out and buy some topical anesthetic, like the stuff sold in tubes for teething babies, and rub it on the sores. It will make you more comfortable, that's for sure.
If you are really worried, go to a DENTIST, who is a specialist in head/neck issues. They know far more about oral lesions than your MD.