She's probably stressed and/or tired. Vaccinations and a trip to the vet can sometimes do that. Leave her alone for the rest of the day & she'll probably be fine by morning. If not, call your vet.
It has nothing to do with the shot itself. Your cat's daily routine was interrupted by the stress of the visit and cats hate change. Let her stay under the bed and come out at her own will.
Yes, but only temporarily. With any new or painful experience, an animals behavior changes for a short while. When she comes out, show her care and affection, she'll be fine.
