Well, these days, most therapists aren't MD's, so they can't prescribe meds. You'd need to see a doctor for that, most likely a psychiatrist. What meds work (if any) and how quickly varies widely from person to person, so there's no hard answer to that question.

As for how quick you get a diagnosis, that varies a lot too. Some therapists don't think a specific diagnosis is all that important, and they choose to focus on the client's particular issues rather than a broad category that may not completely fit the client. Others feel a diagnosis is much more important, and they may do extensive diagnostic testing. It really depends on the clinician.