I recently had unprotected sex with a random girl I met, now my penis ia constantly burning and it wont stop is this bad?

Yes. In this scenario, it is highly likely you have contracted a sexually-transmitted disease (std). This is where some type of organism has entered the urinary tract and will require an evaluation and antibiotics to treat. Using condoms will help decrease the future likelihood of std's. If ley untreated, it may turn into a chronic and more serious condition. Refrain from sex until treated.
Yes, she gave an STD. You need examined by your dr / "std clinic" / urgent care or urologist for diagnosis and treatment for whatever you contracted by not using condoms, particularly during casual sex. Good luck.
GC/chlamydia. You likely have gonorrhea or chlamydia.Both can cause sterility in any girl you have sex with and both can give you symptoms.The GC is more intense and painful for most. Cure is possible but requires you seek out the testing that can allow for the proper medication.The sooner the better.