I don't have one, nor need one but...
what others have said is true...

you can retain one after a hospital stay and often this is a requirement before release, that if you need to be on medication, they line you up with a Pdoc to provide the consults and scripts. Many psychologists have someone they refer their patients too, if they think medication might assist in the therapy process. Some psychologists in the USA have limited prescribing rights too. Your regular MD has a list of Pdocs to refer to, but often that's strictly out of the book type listing with little feedback, imo.

You can check your health insurance providers listing of Medical Doctors-Psychiatry.
In the USA you can check here: http://finder.psychiatry.org/

Personally, I am glad they are "shrinking" breed of doctor. And also IMO they had no business trying to perform talk therapy in the first place. So many were Freud-like in that they let the patient ramble and then they jumped to conclusions and shoved medication... (No, I don't like psychiatrists and have only known 3 in my lifetime that were really great doctors!) BUT if your regular MD doesn't want to handle regular medications for depression, anxiety and the like, you need a psychiatrist.

good wishes