This should NOT be a long term SE of your brachytherapy. Some patients do experience some urinary side effects in the months immediately following the procedure, but those should have subsided by now for you.
Obviously you should see your uro-doc (or another one) to see what is going on...
After Googling "brachytherapy and burning urination", I could not find ONE site that suggested that this SE could manifest itself as long as two years after initial treatment. I'm not saying your uro is wrong, but this just does not make sense. Brachytherapy burning is usually an artifact of the radioactivity in your body. After two years, that has been dissipated for some time.
There are many causes for burning urination (Google it and see) and it is unlikely that 2+ year post-seed treatment is one of them. Since this has been going on for two months and your doc just wants you to wait, if I were you I would seek a second opinion.