I have a burn at the tip of my penis but no discharge. My girlfriend says she burns after we have sex?

Both of u get tested. Both chlamydia and gonorrhea - two types of STDs - can be totally without symptoms, especially in guys! Your girlfriend's symptoms may not have anything to do with yours, but it'll put both of your minds' at ease if the tests come back negative.
Probable STD. You should both be seen medically and both be treated or else you could reinfect one an other. Good luck.