My Reply

I've recently starting seeing a psychiatrist for depressions, anxiety (especially the social variety), and paranoia (that's a particularly difficult one for me to discuss with her).
Did/do you suffer from social anxiety? Evidently, I do. Mostly it's because I have nearly no idea what people are trying to say (I miss almost everything conveyed by non-verbal means, be it eye contact, facial expression, gestures, posture, invasion of air space), and coming up with correct/appropriate responses is nigh impossible. Thus interaction is very taxing and frustrating. -StalinsNotDead

I think you revealed your problems you are facing very adamantly. This is indeed the first and most important step to solving your problem. In order to understand them, we need to share the same ground. When you say you can't understand others, you could solve over the half of problems you had. Because they will start trying to understand you.

She (the psychiatrist) said she thought the non-verbal communication problems I have are developmental (I was raised in a religion that frowned upon non-religion friends, thus had few friends),

Yes, she is right.

and the social anxiety can be dealt with pharmaceutically.

Please keep away from drugs. Only stupid doctor resort to drugs, it is a very bad idea.

I'm wary of the pharmaceutical route, especially considering how quickly the person was to give it out; and that some kind of therapy could help teach me these skills.
Can a psychiatrist make a diagnosis, or does it have to be a psychologist?

I strongly recommend you to consult a psychologist

I'm a bit hazy on the differences between the two.

The difference is apparent. Psychosis is caused by physical contact, while neurosis is cause by meta-physical contact.

I've read as much literature online as I have been able to find, and have concluded (yeah, I know self-diagnosis is worth almost nothing) that I may have a form of Asperger's. Can behavioral therapy help? Has being diagnosed helped you in any way? Are there any books or websites you would recommend, especially on the topic of dealing with neurotypicals?

Non-verbal-tacit, verbal-language, both are meta-physical, this can be cured by psychological approach. Don't worry, you will be well soon, but you need to find a very good therapist. I can help you on line. Leave it to me.