Whether you are eligible is a discussion to have with your own psychiatrist or other mental health provider. The question to ask them is whether they consider you LEGALLY disabled. The legal definition is:
"a physical or mental impairment that substantially limits one or more major life activities of such individual"
"[M]ajor life activities include, but are not limited to, caring for oneself, performing manual tasks, seeing, hearing, eating, sleeping, walking, standing, lifting, bending, speaking, breathing, learning, reading, concentrating, thinking, communicating, and working."
"[A] major life activity also includes the operation of a major bodily function, including but not limited to, functions of the immune system, normal cell growth, digestive, bowel, bladder, neurological, brain, respiratory, circulatory, endocrine, and reproductive functions."
If your doctor agrees that this applies to you, then you qualify.
The difference is in what you want the dog to do. If you want the dog for companionship, emotional support or therapy, then you want an emotional support dog. If there is something you cannot do because of your disability that a dog could do for you, then you want a service dog.
An emotional support animal is basically a "prescription" pet. It means that if you live in housing where pets are not permitted, you can get an exception for an ESA. If pets are allowed, then it's the same as any other pet. Here's more:
http://www.servicedogcentral.org/content/ESAA service dog is individually trained to do something for the owner that the owner is not able to do for themselves because of their disability. This training requires a certain level of skill on the trainer's part and typically takes 18-24 months to complete. If you purchase a dog with this level of training, expect it to cost several thousand dollars. If you hire someone to train such a dog, again, expect it to cost several thousand dollars. If you qualify, some programs will provide a trained dog at a reduced cost by offsetting some of the expenses with volunteer labor and charitable donations. Still expect to chip in around $1,000 of your own money. Here's more:
http://www.servicedogcentral.org/content/PSD