I will share with you how I found my therapist.
I contacted a psychoanalytic institute in the largest city near me and asked for a referral to someone there who does therapy or to someone in my community.
I was referred to my T who was a candidate (student) at the institute; she had been a therapist for over 20 years before being accepted by the institute to learn analysis.
She has a Masters in Early Childhood Development and is a LMHC, Licensed Mental Health Counselor. (I used to only look at PhD Clinical Psychologists, so T not being a psychologist was something I was not sure about in the beginning. Turns out she is the best therapist I've had, and I've had a few. She offers a nice mix of analysis and support )
I was also lucky that one of her specialties is Borderline PD.

What they mean by a higher level of care is a good question to ask the person who says this.

What happens that makes them decide to stop seeing you?