Q. If I have my dog made a therapy dog or a emotional support dog can it then live in a apartment that doesn’t allow dogs?

A. Therapy Dogs are pet dogs that can be owned by either disabled or non-disabled owners.

THERAPY DOG
Per Delta Society:
Therapy animals and their handlers are trained to provide specific human populations with appropriate contact with animals. They are usually the personal pets of the handlers and accompany their handlers to the sites they visit, but therapy animals may also reside at a facility. Animals must meet specific criteria for health, grooming and behavior. While managed by their handlers, their work is not handler-focused and instead provides benefits to others. 
http://www.deltasociety.org/Page.asp…ServiceTherapy

The owner/handler of a Therapy Dog does not have additional rights in Housing or Public Access over any other pet owner.

EMOTIONAL SUPPORT DOG (ANIMAL)
Per Service Dog Central:
An Emotional Support Animal is a dog or other common domestic animal that provides theraputic support to a disabled or elderly owner through companionship, non-judgmental positive regard, affection, and a focus in life. If a doctor determines that a patient with a disabling mental illness would benefit from the companionship of an emotional support animal, the doctor write letters supporting a request by the patient to keep the ESA in “no pets” housing or to travel with the ESA in the cabin of an aircraft.
http://www.servicedogcentral.org/content/ESA

If your treating doctor or medical team deem that you have a disabling mental illness and enters such into your medical records then you may be able to have your dog live with you in no-pet housing. Only landlords in certain types of housing are required to accommodate you and allow your dog to live in the rental.