Nerve problems would probably be best treated by a neurologist and depression can be treated by a psychiatrist, a family physician, or an internal medicine physician, but a psychiatrist might be the way to go for depression.
A psychiatrist is a specialist in psychiatry - the study of the mind and behaviors. They are not family doctors (known as Family medicine specialists). If the psychiatrist were to complete residency training in Family medicine, then he could be a family doctor.
In the U.S., four years of college (with requirements in biology, chemistry, physics and others), four years of medical school, and four years of residency training in psychiatry are needed, in order to become a psychiatrist.
Let's say you start college at age 18. 4 years for your undergraduate degree makes you 22, 4 years of medical school puts you at 26, and 4 years of psychiatric residency brings you to 30 when you become a board-eligible psychiatrist.
No, quality psychiatric care is never free nor online. The sites you get for free care are usually bogus and who you are talking to is normally not a licensed psychiatrist. Its always best to find a local psychiatrist with credentials you can see in person.
The simplest way to describe the difference between a psychologist and a psychiatrist is that a psychologist primarily aids the depressed patient by counseling and psychotherapy. A psychiatrist may also perform psychotherapy; but, in addition, can prescribe medications and perform ECT.