The problem with absconding from meds is that there is a probability that the genesis of your problem is physiological. Although therapy rewires the brain where there is trauma, it is a slow process. And it may not help if the problem is mainly physiological (like chemical imbalances or what have you).
I was an anti-meds person my entire life, until I developed panic disorder. Way before that, I had Graves' disease and mitral valve prolapse. I refused to take pills to decrease my thyroid activity. And I was dx'd. Eventually, it all blew up in my face, causing a thyroid storm, which put me in the ER, and later on, a severe panic disorder.
I even tried curing the panic by going to an endocrinologist, adjusting my thyroid levels, thinking it was completely hormonal. It did not. Not until I was treated by a psychiatrist for panic disorder did my symptoms subside. Therapy (and relaxation and exercise and all that other jazz) is great, but only in addition to the meds IMO.
A psychiatrist is a medical doctor, which is why they can prescribe meds and many have internal medicine experience. They approach your disorder from a physiological perspective.
A psychologist only holds a doctorate in their field and are licensed to practice psychotherapy. They are not medical doctors. I'm not 100% sure how it works, but from what I understand, many cannot prescribe meds (depends on country, I believe).
The difference is a psychiatrist won't spend a great deal of time with you, but they approach your disorder from a physiological perspective while psychologists approach it from a mental disorder perspective. What's that mean? I dunno.
But keep in mind, just because you go to the psychiatrist and they provide you with meds, you do not have to take them. You could keep them as a 'fail-safe' if you decide to go the psychologist route and you're finding nothing is really changing. Plus, the psychiatrist can dx your disorder and recommend the best course of action to take in regards to therapy (remember, there's CBT, EMDR, hypnotherapy, exposure therapy, yada yada). I'm not sure if a psychologist can do that, but if they can, they cannot order medical tests to be done and dx you from that (which a psych might).
Personally, if it's affordable, I would go to the psychiatrist first, get their diagnosis, then find a therapist. A specialty therapist will probably be cheaper than a psychologist. You can always hold off on the pills until you need them. Or take 'em in small quantities. Compromise is good.
If you decide to go to the psychologist, please let us know of your experience. For my knowledge of them is completely theoretical.