Actually, what you think and feel is most important and if you read about BPD and it feels "right" to you, that is important information for your therapist to know, to tell where you are coming from (and why you are coming in). You would follow it by explaining why you feel you might have BPD, what traits you see in yourself.

I wouldn't present it as "diagnosing" yourself but say something about feeling "most comfortable" with that rather than depression or other dx's you've read about.