Your question: My daughter has "mild" asthma and has been working out at a gym. But after working out for a few days she has more tightness and asthma symptoms. This has happened twice (trying different gyms). Her asthma is do to allergies. Have any suggestions?
My humble answer: She might want to back off from the heavy workouts until she works with her doctor and gets her asthma under control. Thankfully there are some really good asthma medicines that allow most asthmatics to obtain control quite easily. I wrote a post on how to gain control of your asthma here.
On a side note here, exercise is very important for asthmatics. It may actually prevent asthma from getting worse. It makes the heart and lungs stronger. So it may actually be a fine balancing act for a while.
Still, once her asthma is controlled, she should be able to do pretty much any exercise. I know, because I used to have a similar problem. Now I'm able to workout and run at will.