AVOID. The best thing would be to work in a different lab without exposure to the animals. If not possible, the asthma is treated with anti-inflammatory, preventative medications and bronchodilators as in all asthma patients.
Seek treatment. Allergy to lab animals can be treated with symptomatic treatments like bronchodilator and steroid inhalers as well as allergic desensitization, typically performed by an allergist after allergy testing is done. See your doctor for evaluation and treatment so you can hopefully keep your job!
Avoid. Avoid lab animals, pets, or anything else that triggers your occupational asthma. People with occupational disease tend to do very well when they find another line of work. If you can not, for some reason, do so, try working with an allergist to get desensatized - but this is usually difficult for occupational disease.