JoanWLaura,
I remember occasionally experiencing the same kind of burning pain after urination when I was probably about four or five years old but I don't recall if it occurred at any particular time of day. The pain was localized at the opening of the urethra so my doctor suggested pouring warm water over the opening while I sat on the toilet. I guess that helped since instead of lasting for hours as you describe, the pain was gone after what was probably 10 or 15 minutes. I don't know how long it continued to occur but it probably was not too long since my memory is vague except for the pain itself and the relief that I got from the warm water. As a clue in your search for the cause keep in mind that although I am a salt waster, I never took florinef as a child so you can probably rule out florinef as a factor. It was definitely not the same as a urinary tract infection which thankfully I have only experienced twice in my life, once in my twenties and the second time only a few months ago.
I bring that up because I have something that may help you and anyone else who suffers from urinary tract infections. I had read that cranberry juice prevents the bacteria that cause those infections from attaching to the wall of the bladder and urethra. Since commercial cranberry juice is loaded with sugar I tried a cranberry supplement that I bought at a heath food store. The one I tried was called CranMax and only required one capsule a day. In about 3 days I was free of all symptoms but to be on the safe side I continued to take it for another few days. It may not work for you but since it only contains "standardized fruit extract and whole fruit" it can't hurt and it's something to try until you can see the doctor and get a prescription filled.
I hope this helps.
Joan