I would do a test...try increasing water intake for the first half of the day and see if it helps dilute the urine enough to ease the burn. You won't be harming yourself by choosing to drink moderately elevated levels of water. If this does ease the discomfort I would say continue drinking water as you see fit, while making it a point to eventually return to the ”water when thirsty” practice.
If that fails, I would go dry for the better part of a day and see what kind of results your body achieves.
Kudos to you for choosing to turn to fasting to alleviate your physical issues. I'm extremely interested in your developments and wish you the best!