I feel your pain, bro.
I'm a chronic asthmatic. I'm much better than I was 20 years ago, but I'm still considered "chronic". It really messed up most of my goals in life, from wanting to join the army ever since I was a kid, to just learning how to scuba dive (Which I finally did two years ago by not disclosing my condition on the forms).
With most activities, I'm generally OK. I jog, weight train and do other cardio workouts 99% of the time with nary a wheeze. It's allergic reactions that are my kryptonite. Being allergic to pollen means that getting into the wilds comes with a lot of wheezing.
I use the steroid inhalers and I've tried lots of herbal, alternative, etc treatments over the years, including acupuncture (What a waste of money that was).
The only thing that I found that comes close is eucalyptus. When I find it hard to breathe, if I relax, sit calmly and breathe in eucalyptus, it eventually helps with my airways. The main problem is having the time to do that. If I'm by myself in the woods, then I can sit for 30 minutes to an hour and get over it. If I'm with others, then the inhaler is the fastest and most effective way to get over an attack. You could try a eucalyptus airspray or aromatherapy oils before you work out, or even in the room you workout in. Often this kind of preemptive course will prevent an attack.
As to any kind of SHTF scenarios, eucalyptus may be as rare as inhalers (Depending on your location). The only thing to do is stockpile and rotate. I keep inhalers at work, in the car and more at home, along with bottles of eucalyptus.
One thing that I learnt over the years is to just deal with it. If you have a niggling wheeze, try to ignore it. Don't reach for the inhaler every time. Either relax or try to carry on. It's like any other disability. The more you train your body and mind to cope with it, the less dependent on drugs or help you'll become.
I know I haven't been much help, but good luck to you.