You should definitely visit a dentist. It may appear to come and go, but it can't go away on its own.

Might not be infected. Might not go away on its own. Best to see your dentist for a diagnosis.

If it is infected from the root canal, you need to see an endodontist (root canal specialist) asap. The pain may go away, but the infection doesn't. If it is a periodontal infection (gums), then it may clear, but really, it should be checked out. Again, the absence of pain does not mean it is healthy.
Good luck.

Although anything is possible, it is unlikely that an infected tooth will go away on its own. You should visit a dentist to determine exactly what is going on and figure out the best course of action.