Yeast infection, they sale over the counter medications like Monistat, but of this doesnt work then you should see your GYN doctor for something stronger, sometimes the infection can only be cured with a stronger antibiotic. You can also fill up your tub and but water and vinager to soak your irritated area in the mean time.
I agree with lucky. Was the sore there before you started scratching or after? If the sore was caused by your scratching, it could also have started out as a yeast infection or UTI since it sounds like you were pretty itchy down there before it started burning. There are kits at the pharmacies that can check for yeast infections and UTIs. I've never tried them so I don't know how well they work. If I were you, I would keep the sore clean, get some vaginal anti-itch cream, and if the itching or sore don't go away in a day or 2, go see a doctor.
As far as the burning goes, the pH of your urine can range from 4.5-8 (give or take). Urine, especially when it's super acidic will cause any open wound to burn. Try and keep the area clean and hopefully it will clear up in a few days. Just like Luckytwice said, put some Vaseline on the sore before you pee to protect it and that should help with the burning. Good luck!
sounds like your peeing on skin rubbed raw. Put some vasilene on it and leave it alone for a while. You could have caused an infection in your urethra franklin as well.