Certainly, a broken tooth could cause bleeding from the nose.
The Lexicon will help with any pain or inflammation.
I would ensure he is able to eat and drink, is passing normal stool and is active.
An injury like a broken tooth can take a few days to heal and he may have knocked the tooth again with his tongue or on his cage.
Also, sometimes when their heart rate goes up when they are running about, this can cause bleeding to start up again.
If possible, try to convince him to rest up; easier said than done. Have in a quiet and dark room.
The bleeding should stop soon but, if it doesn't, it is best he sees the vet again.
We would need to consider an infection or growth if the bleeding continues.