
First I would take her to A and E or use the out of hours service and see what either of those will do that would take you out of her doctors immediate care and budget I have had quinseys as a child and its awful poor girl. Just realised this is the same daughter who had all the problems with wound care she really is having it bad :(
Totally ridulous about cost ! of course they could prescribe both its down to the practice what they are doing. Have you spoken to the practice manager/ senior partner
Alternatively I would think about changing your doctor especially given previous problems. I am not sure which part of the pct oversees gp practices but you could try googling and see what you can find
Last resort if you have the means is private care but it shouldnt come to that