I would not care what the vet said....I would take her in for an exam if she is that lethargic!!
No it does not sound like an anaphylactic reaction, but it does not sound normal.
I don' t know why some vets continue to give multiple vaccines.
This is not recommended anymore. which ones did she have?
I also would not cover her up in front of a space heater...she could overheat! Sounds a bit much.