Hi there, I recently went down this road and I did receive my medical, despite having a past history of SSRI usage. It really depends on what type of medication you were prescribed and how long you were on it. Not having your medical records certainly adds a level of complexity to the situation. In any case, it will take awhile but there are ways to help expedite your case from my experience which are...
1. Call the Oklahoma City FAA medical office daily (you will need to call 8-10 times at random times to get through once)
2. Call your Regional Flight Surgeon. They are a massive help and answer much faster and can pull your application.
3. Answer each request letter FULLY and you will likely receive your medical. The FAA is super black and white.
I imagine in your case they may ask you to see a board certified psychiatrist for a fully evaluation if you are unable to have your old prescribing doctor verify your past treatment.
As far as flying, I kept flying twice a month just to keep proficiency because I was already almost 20 hours in. If you are just a few hours in, just take time off and save yourself money and restart when you have your medical.
Good luck!