Happy bday to your sweet girl
!!
Yes, absolutely she could be refusing food bc of tooth pain. I don't know if you've ever had true tooth pain, but it can be excruciating...so I'm glad you're taking her in. Once they get in there, if more teeth need to be pulled - I'd get them all yanked bc the charge per tooth usually isn't exorbitant, relatively speaking.
And yes, the wetness on one side of her mouth could very likely be from that bad tooth and drooling from mouth pain.