It is clear your doctor is not an employment lawyer. It is not illegal for an employer to ask what your condition is - though they probably can't force you to give you an exact answer - and rather than you demanding a certain accommodation and your employer giving in, you are required to be very specific in what limitations your condition causes and then your employer may have to find a way to accommodate you. It does not have to be your preferred accomodation.

Also, you have to be sufficiently specific in describing your disability to establish that you are a covered employee under the ADA! "Medical conditions" aren't covered, "disabilities that meet the ADA's definition of a disability" are.

This is the federal ADA (and though FMLA is different, it also requires more than "I have a medical condition and need time off, thanks"). I am not familiar with NY state law on the issue.