I'll start with a few questions. Do you have a nebulizer to use? How did you make it working in the garden center this summer? That would have killed me, seriously. Does lifting bother you? Were you working at Wal-Mart before you had asthma? If so, I would have your doctor write a letter or even write out on a prescription pad what you can and can not do, what your limitations are. Because of the American Disability Act, they have to place you in a job where you can function without damaging your health.
I was working as a secretary at a local university before I was diagnosed with epilepsy in 2006. In the summer they started cutting the air condition off several times during the day to save money. There was no way I would work in an office with no air condition. I had a couple of asthma attacks. My doctor wrote them a letter that I had to have air conditioning. They started trying to find an office with air conditioning to relocate me, but you see, they were doing this campus wide, well, guess what, they turned the air conditioning back on in my building and it stayed on. They are aware of ADA.
You may have a bit of a battle on your hands with Wal-Mart because they are so big they think they can get by with anything. But, please remember you have your rights. Please don't let them bully you. Start out talking to them nicely and see how it goes, then get that letter from your doctor and remind them of the ADA. They will certainly understand that. Asthma can be deadly. Please keep us posted and if you need any more help, let us know.