Go to immigration, get a letter stating proof of residence, take it to the bank, BB in my case and job done! Couldn't be any simpler. I got one on a 60 day visa. No agent required. What reason are they giving you for refusing?
From my experience of Thai hospitals, I've had reason to be an in -patient a couple of times upon payment you are given a copy of everything and 5* treatment.
I hope you get to the bottom of your health problems and get well soon.