Are there any ways to remove or treat a cavity without going to the dentist?

No, there is no way to get rid of a cavity other than going to a dentist. There are ways to help the pain temporarily if it's needed, but only a dentist can remove the cavity.

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And even when you get rid of the pain it doesn't mean that the problems with the cavity have stopped. The bacteria that causes cavities are not removed by the pills that ease the pain. If you don't treat your cavities you can easily end up with total prosthesis by you're 50. You can see this video for more info on cavities -

http://www.checkdent.com/en/videos/tooth-cavities-89.html