Employment Law Questions? Ask an Employment Lawyer.
Is this recommendation based on a disability that you possess?
Did you state that you were making the request under the ADA, and that you were requesting a reasonable accommodation?
Have they allowed others to work from home?
I understand it is based on a doctor's note, but that is not controlling. Doctors can't impose things on employers. They can make suggestions, but just because a doctor said it, that doesn't make it mandatory.
I don't say that to say that your situation is not strong, but just to be clear about the law. Your doctor here has made a recommendation based on your disability and you asked about an accommodation. The employer then is on notice that the ADA is in play here. If the employer has allowed others to work from home, they will be hard pressed to say that this is not a reasonable accommodation (as it has been reasonable for them in the past).
Your next step then is to file a complaint with the Equal Employment Opportunity Commission. That agency can review the facts, and your request, and force the employer to explain why they believe your requested accommodation is not reasonable. The EEOC can also give you the right to sue. Preserving your rights here requires an EEOC complaint.