Stamina Up

I have been training for about 8 months now, and my stamina always have been one of my main concern. I suffer of light asthma and I don't really have any problem until I do intense anaerobic exercise, for example sprints.
When I first started training I have a couple of episodes when I have not eat anything and felt dizzy to the point I was about to faint. So I would stop and go home. In my gym we warm up by doing 3 x 3mins rounds of skipping with sprints every 20 seconds for 20 seconds. Within rounds we do 10 burpies, 10 press up, 10 push up and 10 squats. After this we do shuttles for 2 minutes and 2 minutes shadow boxing for 3 times.
I recollect that at the very beginning I was barely able to skip, and never done any of the sprints. In between skipping rounds I was barely able to do all the sets and my legs felt so heavy, and during the shuttles I wasn't dashing instead just jogging back and forth.
After my first interclub I felt powerless and out of breath to the point that I was about to quit at the second round. When I was back to training I started pushing my self up during the warm up so that I would be able to do an interclub without struggle.
So I started doing sprints during skipping which I never used to. Of course beside the extra effort I put I still had 6 months of training behind me, but just recently I just thought of the progress I made. In fact we sometime do 5 rounds of skipping with sprints, and I do all of them! Between rounds I use to barely get to the end of the set of burpies and all, and now I manage to do it under the minute so I can start the new round of skipping on the zero mark on the clock.
It took a while, its true, but perhaps if I would put a bit more effort before, my stamina would have been even better.
This is reflected on pad work as well. Before if I had to do sets of 20 kicks per leg on the pads, I would have to take a break because I could not breath no more, but now is way easier.