It looks like you want to know two things: does she really have asthma, and will the inhaled medications hurt her? As for the first, as a mother of a child with asthma, it seems really clear that your child does have asthma. It's a shame that it took so long to get it figured out -- she should have been on preventative meds starting a long time ago, and because she wasn't, she had lots of unnecessary attacks.
So first of all, take her to an asthma specialist. Your doctor isn't doing enough for her.
Second, the meds she's taking are safe, and are totally necessary. There are two types of meds she needs -- the ones she takes daily to prevent attacks, and the "rescue" meds she'll need to help stop an attack once it occurs. If she takes the daily meds, her attacks will become much less frequent.
There are plenty of websites and books out there to help parents of children with asthma. I found them really helpful. The thing about asthma is that the parent plays a really important role in recognizing symptoms or problems and responding to them the right way, right away.
Good luck!!