Update.

Went to the doctor again today.  He was an idiot, but basically said that if I've taken amoxycillin before and  it was fine then it should be fine now, regardless of the adverse reaction to the penicillin.  So I got amoxycillin.  Took it.  Red puffy face, hives, and an itchy neck is what I have now.  And that doctor's appointment cost be £50!  So I'm sucking it up and taking it.  Another day off school tomorrow as well, as my head teacher said not to come in.