Teething at 3 Months?

First time mom here. My 3 month old daughter has gone from a giggling and social baby to a teary-eyed drooling screamer who constantly chews on her fingers and refuses to be put down for any amount of time. All signs point to teething, but everything I've read says this would be abnormally early. I called my pediatrician, and the nurse just said it's unlikely and wasn't super helpful. I'm at a loss, as this behavior kind of appeared out of nowhere.