Does it hurt more on opening and closing the hand? Is it tender to touch?
Tendinitis usually will hurt more by causing the tendons to move, like when opening and closing the hand.
A local soft tissue "bruise" will just be tender to the touch.
Rest and ice are usually the first treatments for any type of inflammation.
Do you play with a padded grip? Would you consider using one for a short time if the problem seems to be more of a "bruise"?
It sounds like you really like tennis.
If this is persisting despite rest, a proper exam by a hand specialist would be in order, rather than risking this becoming a chronic problem.