I have added several tags, as this is not a malpractice question, and you will get better answers from attorneys who deal with employment and hiring practices. I would think that perhaps a letter from your physician may help depending on how the nicotine is ingested. Hopefully you can get this worked out. I understand and empathize with your dilemma.
You will want to report this question under employment law to get a better answer.
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I've changed the practice area for you to employment law, so the employment/labor lawyers can chime in
This is general advice and does not establish an attorney-client relationship.
If you have a diagnosed medical disability which can be the subject of reasonable accommodation and the method of accommodation is not one that is a overly burdensome upon the employer the employer may have a duty to accommodate. As things sit right now you may end up with a proof problem. Start a file beginning with the advertisement or your method of finding out about the job and create a timeline of all your activities and contacts to date and consult an attorney immediately. Whether your potential issues are going to be the subject of an EEOC (Federal) investigation or a State (Human Rights Commission) investigation (or potentially no state or federal investigation and only a private right of action) will depend upon the number of employees. The short answer to your question is that it is very possible that if you are not hired because of a medical disability that you may have recourse. When you either call government agencies or see an attorney one of the first things they are going to want to see is the medical proof of your disability and then they are going to want to know how you can prove it is this specific issue that is causing you not to become employed. There are deadlines to file complaints with the EEOC and HRC so I would act promptly on this.