Will it hurt me if I swallow tonsil stones? Do they ever go away

No and yes. Tonsilliths or tonsil stones are an accumulation of debris in the crypts of the tonsils. They cause discomfort and foul breath. They can be expelled with blunt end of a toothbrush or like object. If swallowed, they are readily inactivated by the acid in the stomach. This should not be harmful. Good oral hygiene, gargles with most gargle solutions will help. You may end up with tonsils out.