Personally, I wouldn't you use the 消炎药 from back home as it would not help and shouldn't be depended on. And even if it work, it would be too late anyway.
Although they said the sickness should go away in 3 weeks, and if your daughter remains sick after two weeks, then you should take her back to the hospital to check out again just in case.
Note: New immigrants tend to feel bad when they think they shouldn't go to the hospital too frequent. Please don't, if you feel your daughter's situation is getting worse, then take her there anyway. If won't hurt to just do the checkup. This is a dangerous time due to the swine flu, so you should be in high-alert.
If you need someone in Chinese translation at the hospital, send me a 悄悄话 and I could help you.
Actually, this is just the opposite, it was reported by one of the TV stations (I think it was CBC a couple of years ago) that the Canadian doctors prescribed too much 抗生素.
If you are not comfortable with it, tell your doctor so.