So first, I love your research, though I'm sure you did some of it out of some anxiety. But good for you for finding all the stats. :)
It doesn't sound like what you have is syphilis, though you could certainly get a test to find out and put your mind at ease. Most people will test positive by 6 weeks, which is just where you are now. It's a simple blood test - as I'm sure you know - and then you can put this behind you.
The timing of your sore fits for syphilis, but it healed too quickly for it to be syphilis, but I can understand why it crossed your mind.
Have you ever seen a doctor about how you feel when you pee? How is your water intake? Caffeine and alcohol intake? Increase your water intake, and decrease the other two and see if that helps. If you drink a lot of caffeine, decrease that slowly or you'll get a really bad headache.