Legal Question in Employment Law in Ohio

Unless you have a contract or are in a union, you can be fired for any reason or no reason at all so long as it does not violate an anti-discrimination rule or other law or public policy in Ohio. Generally there is no law allowing you to wear perfume or cologne. Unless you are a contract employee, have a collective bargaining agreement, or this policy is enforced in a discriminatory way, there isn't much you can do.

You can be terminated for "annoying" your co-workers with your fragrance. If the fragrance is related to a disability you may have, you may also be protected. But again, your employer does not need a reason, generally, to fire you. Without knowing more, I cannot give you specific advice. However, it may be a good idea to do what they say--there is a lot of stress involved with finding a new job.