11 week old teething?

My daughter is 11 weeks, about to turn 12 weeks on April 2nd and I think she’s teething already. For the past week she’s had these symptoms:

- constantly drooling (sometimes have to change her clothes 3x a day because she soaks the collars of her outfits)

- always chewing on hands

- wants her paci more often (usually only uses it at nap time/bedtime)

- sucking her fingers

- sucking on her bottom lip

I have felt inside her mouth with my finger & her gums are hard. Is it possible for babies to start teething this early? If not, what could be causing her to do these things? Any advice is greatly appreciated. ☺️

Bonus question: do I have to take her to her doctor to confirm that it’s teething?