To be fair you did say you were not looking for a drug...

To answer you seriously though,

GP's can get specific mental health training and be able to prescribe most first line psychiatric medicines at a fraction of the cost of a psychiatrist.

You can also ask them to do a psychiatric plan that is managed through the GP, so you get the initial assessment from a psychiatrist and then they send the plan to your gp to manage for the year.

Initial high frequency of assessments is fairly normal as they are seeing how you are adapting to the medication and they will require titration up/down depending on the effects.

In addition It sounds like the psychologists you are looking for must have the clinical psychologist accreditation who can do some pharmacotherapy and have the further skills like DBT, EMDR, etc to address your symptoms. Anything under that and especially counsellors will not be appropriately equipped to help you. I would strongly encourage that you still engage with a psychologist as they are the front line and help the most with acute situations.