You could bring a complaint to the federal Equal Employment Opportunity Commission (EEOC) or your state's equal/civil rights agency. The law requires a "reasonable accommodation," or a not-too-expensive change to the workplace or your job, to accommodate a medical condition which is serious enough as to affect some aspect of life: a bad allergy could qualify. A reasonable change or accommodation would be to not have an office cat, since there is no need for one--eliminating something unnecessary at work to help an employee's medical condition and let him/her work without suffering or impairment is certainly reasonable. You may be entitled to compensation, and/or the agency may force the employer to get rid of the cat.