Have you tried running in different climates? It may be the air temp or humidity that is hindering you. Just a thought.. I know the cold air can really suck the wind from just about anyone
Actually, I do better in warmer, more humid climates. It's something about the way you move, since I've also tried treadmills indoor, along with running indoors during PE, and I just can't do it. Even though I can really get going on a bike, just something about the motion of running disagrees with my lungs. I can't do aerobics, either. When I took PE in middle school and freshman and Sophomore years of high school, we had this test called the pacer where we would run across the gym as many times as we could, gradually increasing pace. I would find out the passing amount of laps, go for that long, then take myself wheezing down to the nurse. Finally, my doctor said, "Don't do that! All you ever do is wheeze during that!" so I got out of it for high school. I was so sorry. Not. They still made me do the mile, but I was allowed to walk it and jog if I felt able, which sometimes I did. I used to beat some of the kids who actually ran it. It was funny.
Colder climates trigger me, so you are on the right track. I can't exercise outdoors if it gets below 50 degrees. So basically I don't do any winter sports. During "Snowmagedom" I did not leave the house for two weeks. I stayed inside and avoided the snow and cold weather.
My dad took me bike riding in the campgrounds and it was 100 degrees that day, and I had absolutely no trouble, though I made him stop about 5 times because I felt like I was drowning in my own sweat. We check the weather before we go now. But yeah. No running for me. Been that way even when I was in first grade. I would run, cough, then stop. Didn't even know I had asthma then. So I do what I can. I can use a stationary bike, get my heart rate up to that of a run, and not wheeze, or I can run, feel like I'm dying, and then wheeze (even with a preventative inhaler) and then have to take more medication. I can also swim laps with no trouble, do Pilates, jump on a trampoline, and do some dancing (not super fast, though, and with frequent breaks). So if I'm never able to run, I don't think it will ever be a terrible thing.
Like the doctor said, if it hurts when you move your arm that way, don't move your arm that way, if you wheeze when you run, then don't run.