No not a self test: you need to be tested by a professional. It's done in a sound proof booth using a standard set of tests, including mechanical things like measuring how well your eardrum responds to sound vibrations. I think I pay ~$75-$100CAD per checkup.

You usually don't need a referral as most hearing aid clinics will just let you call up and schedule an appointment. If you want to talk to an ENT specialist though, you'll probably have to go to your family doc first.