2 month old teething?

He will be three months on march 10th. Anyways. He has been drooling excessively,fussy the last couple days,& putting his hands in his mouth. And he sort of bites on his hands...if that makes any sense. Also i suspected he was teething so i put his pacifier in the freezer for like two minutes gave it too him he calmed down..then as soon as it wasnt cold he flipped out...is he teething or what is going on. He also has thrown up a lot today. No temp though