I don't think that your T is doing you any favors. They are working for you not the other way around. Therapists cannot give you a diagnosis but they can help to provide a means of education in dealing with the diagnosis via CBT or DBT or some form of therapy.

My own T has said to me that any good T will be trying to do himself out of a job. Meaning he is there for a time to teach skills to people how to live life to the best of their ability, not to be a permanent fall back.

A psychiatrists first appointment with you will be more that 15 minutes and they should take a history and come to a some form understanding of life through your eyes. You may or may not have BPD. You may or may not have type 1 or 2 bpd.

There are meds that that can ease the stresses, high and lows. Whether you choose to take medications is up to you. Nobody is going to force them upon you. The doctor that suggested you see a p'doc is well trained and I doubt would do it if there wasn't a need. Do you have a family member that might see how your life is being affected?

Where I live there are P'doc's that will see you for a short period and others that will also provide therapy at the same time.

Couldn't hurt to get a second opinion from a p'doc. What you do with the information from there is up to you. Wouldn't hurt to see another T either.