References, Credit Checks and Background Searches
These days, employers not only check an applicant's references, they also check credit rating and background.
Carefully consider who to list as a reference. Then speak with the people you choose to ask them if it is okay to use them as references. If your references know about your health condition, tell them it is not relevant to the conversation. Ask them not to bring it up -- unless they are asked. Even then, they should confine what they say to general statements which relate to your ability to do the job in question rather than the details of your diagnosis or symptoms.
Ask your references to contact you if any prospective employer contacts them so you'll know what your prospective employer knows.
Also do homework about your credit and background. Find out what a prospective employer will learn. If it's negative, consider bringing it up yourself with a positive spin. Sound planning will pay off.