The bleeding could be due to depot shot, frictional injury due to sex or because you just started your periods or because of infection or because you finally broke the hymen. Take a pregnancy test and if it is negative, please discuss with your doctor. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.
Visit a gynecologist. She will help you identify the root of the problem as bleeding during sex is never something that's good.
Also, maybe the absence of lubricant without a condom led to tearing? Use more lube! When you have sex, you might not be producing as much lubricant naturally as you need, and a water based lubricant will make you feel better. I've experienced this issue before and it's common.