Sorry to hear you're having so many problems with your new health insurance. Unfortunately, while kids under (I believe) 19 are now covered by the "no pre-existing conditions" clause in the AHCA, adults have to wait until September 2014 for that to kick in.
There are many pharmaceutical companies that are trying to help out with problems like yours. If your asthma is as bad as you say, your doctor might even consider you for Xolair. It is extremely expensive, but if you qualify, Genentech will provide it to you free of charge. I don't know if your asthma doctor is aware of the program, but if so, he/she might be interested.
There are other health assistance programs. Actually, when my insurance company refused to cover something, they gave me the names of a couple programs like that for me to check out.
I would guess that other companies will provide drugs for free or reduced charges.
Good luck in your search for answers. Hang in there. In just a few months, there will be a lot of other insurance options and nobody will be able to tell you that your pre-existing condition is not covered. However with your high deductable prescription drug plan, I'm not sure how much that will help you.
Once the AHCA starts up fully in 2014, there may be an insurance plan in the insurance exchange in your state that will work better for you than the one you're on. I don't know how that will work. Also, I'm not sure if it will force your insurance company to provide better coverage at that point. Good luck!