Asthma symptoms until the next day? That sounds scary.
I have asthma and since dropping weight it is way more under control. I managed to exercise by talking to my Dr. about controller meds. At first I was using my rescue inhaler way way too much, but I figured out a good combo of meds so I only needed the inhaler when I pushed it too hard in cardio.
Are you on any prescriptions right now? Controller meds are your best friend. Also don't think you have to kill yourself on the treadmill running full speed. Depending on your fitness I say take it slow and gradually build up to what is comfortable. I find there are fewer attacks this way and it's easier on your airways not to be sucking in air so rapidly. If you get too winded just ease down a bit. This was what worked for me and I haven't had an attack in over 6 months.
Good luck!