I think shes way too serious too early on

I met this girl on a night out and we hit it off pretty well. I saw her the next day and ended up taking her home, then we hung out all day the next day too. I did tell her i do fancy her and she said she likes me too but shes telling people im her boyfriend and stuff already. Not that i dont want to be her boyfriend but i feel like i need to know her a little longer to put a label on it.

Also she seems really into pda i like holding hands and stuff with her but shes wanting to neck on with me randomly in public. like its not that im embarrassed it just feels weird having her tongue down me throat at half 2 in the afternoon in the middle of town ykwim

am i being a **** or is this a normal reaction idk