It is not clear from your question whether you are a male or female, which obviously affects the answer to your question.
However, there are a few basic observations I can make.
First, urinary tract infections are common after sexual intercourse, especially in women. These can be associated with burning with urination as well as a bit of bloody discharge.
Similarly, various sexually transmitted infections could cause burning and bleeding
Finally, there could be some local trauma from sexual intercourse. Again this is more common in women, since the vaginal mucosa is very delicate and can be easily lacerated.
Regardless, the first step is that you must go see your primary care doctor
as soon as possible. They will be able to examine you for any signs of trauma. Also, they can take a look at a urine sample and analyse it for any signs of a urine infection or a sexually transmitted infection. Based on what they find, they may decide that you need a prescription for an antibiotic to get rid of an infection. In the meantime, it would be best to avoid sexual intercourse until you are seen by your doctor just in case this is a contagious problem.