What if you agreed to get the shot in exchange for the dog not sleeping in the bed? That would be a compromise.

There may not be enough room on the bed for a dog and two people, so it's the kind of problem that can go away on it's own after she spends a night or two unable to sleep. Also, you may find that the dog on the bed doesn't bother your breathing - or you may want more room. I would not have this fight until it actually happens. You can always kick the dog off the bed when your GF falls asleep, too.

I think the bigger issue is going to be all the dog hair/dander in the apartment, not where the dog sleeps at night. Do you have a backup plan in case this doesn't work out for you health-wise?