First of all, I’m not a doctor and don’t really know what I’m talking about. If the pain is lasting for 6 hours, I would absolutely recommend going to the clinic. They won’t look at you funny. They treat this type of thing all the time.
With that said, I used to have a similar issue. It didn’t always happen, usually only after a second or third round with my girlfriend. I described it as more of a discomfort than burning. The best I can figure is that not all of the semen escaped the urethra during/after ejaculating. For me, it usually went away after I took a nice long piss to clear it out. I finally got tired of it happening though and found a solution that works for me;
The most important thing I focused on was training my PC/BC muscle. By having additional control, I was able to build up the intensity of my ejaculate (not to mention lasting longer during sex). Check out westla’s Locating the bc muscle to read more. Also, do a search for ‘kegel’.
Another variable that seemed to help was taking a piss before sex (or masturbation). Not exactly sure why it helped, but I never seemed to get the discomfort after ejaculating if I took a piss 5 minutes before sex.
Finally, drink more water. I used to be real bad about not drinking water and the quality/quantity of my semen suffered. Try to drink at least 4 tall glasses of water a day (if not more).
Again, this is just what worked for me in my experience. I’m not an MD and still think you should go to the clinic. Good luck!