In college, you do not usually need to tell the professor what your disability is. How much you reveal about your challenges is up to you. If your issues are health related and may affect your attendance, you need to go over those problems with the Disability Office and follow their recommendations for discussing matters with the professor.
Sometimes the disability issues appear obvious, but not always. I have had students who had obvious physical disabilities, but also had Learning Disabilities that were not so evident. How much you reveal about your disability is something you need to come to terms with. I have known students who don't care what anyone knows, and I have had others who do not want anyone to even know they have a disability.
My recommendation is to speak to the professionals at the Disability Office and discuss your concerns with them. Many times they can talk to a professor about your needs without revealing anything about your disability. If you feel that a professor is asking questions that you do not want to discuss, kindly respond that you are a private person who really does not want to discuss personal things, and then let the people at the Disability Office know about the professor's questions. The Disabilities Office professionals should know how to handle those kinds of situations. If you are still not pleased with things, follow up again. You may need to speak to the Student Services dean about your concerns.