I have a hole in my tooth - does gum help relieve the pain?

Doubtful. Be seen by a dentist to have it taken care of before it becomes a major emergency.
Probably not. Gum probably won't help. If you have a hole in your tooth then you probably have a cavity. You should go see your dentist immediately, the only way to alleviate pain from a cavity is to get it taken care of and get a filling. Take otc pain relievers, such as ibuprofen, in the meantime.