I applaud you on seeking help as a medical student and being candid. In the end, I'm positive you'll be better off because of it, and if you intend on going into psychiatry, you'll have a huge leg up in terms of psychotherapy acumen. In fact, many mental health professionals end up going through long stints of personal psychotherapy or psychoanalysis and write it off as a business expense on their yearly taxes as it can technically qualify as a training expense. There really is something to be said for experiential learning, and I'm glad you aren't shying away from it.
I'll give you my experience, being in similar shoes years ago. During the start of M1 year the psychiatrist that I saw ended up later taking the job of assistant clerkship coordinator during my 2nd year, with the psychologist I saw being someone I'd end up working with for a couple days during my 3rd year rotation. Even though I tend to be a very candid person, it really did end up being a bit awkward when I entered my 3rd year psych rotation for two reasons: One, because of grading and the awkward "I know something" looks we'd give each other during the clerkship but didn't acknowledge outright (probably should have), and two, because after seeing them for a few months, I ended up transferring my care to a private psychologist and psychiatrist given that I didn't particularly care for the style of psychotherapy and medication management I was receiving. I ended up speaking with my med school counselor who recommended a private psychotherapist whom I saw in the community for a couple years. This ended up being a fantastic fit, as she had current and prior experience working with fellow med school colleagues. After a couple years of seeing her, I transferred my care again at the start of 4th year to another private practice psychologist who offered a different approach (positive psychotherapy) as opposed to the standard CBT-based therapy which I'd become accustom to.
Through these experiences, I've become much more adept at psychotherapy than some of my psychiatry-destined classmates and even some residents.
Now personally, I wouldn't go out and put such experiential learning on a personal statement, residency app, etc.,though I'm sure some have with success. However, I do share my experience with some psych residents and attendings after feeling them out, with the result being very positive and both personally and educationally rewarding.
In terms of finding a psychotherapist, I'd suggest speaking with your med school's counselor and also checking with the providers on your insurance panel for afternoon/evening/weekend availability, as well as a location close to you. The more convenient it is to go to weekly psychotherapy, the more likely you'll consistently go, and the more benefit you'll receive. There's even a study on this that demonstrates a correlation between treatment outcome and miles from home to the therapist's office (pretty obvious, though an important thought to keep in mind).
