What could be the cause of sores on the gums? (if everything with your teeth is fine...)

Ulcerations. Apthous ulcerations are one possible explanation for sores on the gums. Trauma or localized reaction to an irritant are other possibilities. Use warm salt water rinses and give it a few days. If the pain is severe or persistent, get to a dentist and have it checked out.
See your dentist. Multiple things can cause this. It may be a virus of some kind, or it may be related to a more general health problem. It would be best to visit your dentist.