Teething and Tylenol

Ma

My baby just turned 3 months and has started teething. For two nights in a row she woke up to eat around 3am, as usual, but wouldn’t stop moving in her sleep after that. I know she’s moving from discomfort because she puts her hands in her mouth and chews in her sleep. Last night I tried giving her Tylenol to maybe help with her pain in her sleep and I found the same result. Does anyone have any other advice? Did anyone else try Tylenol and it not help relieve teething discomfort?