I don't know if anything I say will be appropriate for you, so check with your doctor.
I find if I have a viral infection, or what seems to be a viral infection, I have to take prednisone initially for the asthma, but when I go off of it, the asthma symptoms come back. So, I'll watch my peak flow carefully, and take neb treatments aggressively and get off prednisone. In essence, I'll depend on the neb treatments to keep me breathing and stay off prednisone so my immune system is not so suppressed it can't fight a virus. This normally works in my case, but if the peak flows starts dipping again in spite of neb treatments, then I have to briefly go back on prednisone. It ends up, in my case, being a situation where I have to walk a tight rope, suppressing the immune system enough to control asthma, but not so much that it can't fight the virus.
In terms of antibiotics, if it is viral, they don't help. They usually only work with bacteria. I'm more fortunate than you as I can use Levaquin if nothing else is working.
The only other thing I can think of is to limit asthma triggers as much as possible. I have found that if I have limited triggers in other areas (pollution, food allergens, cold air, etc.), then the lungs don't freak out as much with a cold.
I got tired of using the medications and getting sick a lot, so I just look weird and where a mask-sometimes a normal mask that blocks only bacteria, and sometimes N95 which has a viral shield on it. I look weird as hell, but I've not had a respiratory infection for over two years.
Don't know if any of this helps, but I hope it does. I don't know what will work in your case.