Can my employer fire me for my asthma?

Yes. Tennessee is an employment-at-will state where you can be terminated for good reason, bad reason or no reason at all.  It is possible that your asthma might be a disability under the Americans With Disabilites Act.  If so, the employer would violate the law if it terminated you because of your asthma.  However, if the employer terminated for something else such as leaving the workplace during schedule hours, then there maybe no violation.  If you want to pursue this matter, schedule a consultation with an experienced attorney.