Baby teething at 3 months old?

So recently within the past maybe two weeks my daughter has been putting her hand in her mouth and sucking/chewing on it. And last night she started to scream cry like she was in pain. Nothing settled her. She’d cry and cry and then be ok for a few minutes then all of a sudden erupt again. Same thing happened tonight. I’ve given her Motrin both times and put her to bed after nursing and she’s been sleeping like a rock.

She’s also drooling and has a slight rash around her mouth I’m guessing from the drool because it was gone this morning.

Has this happened to anyone else?