Your concern for something not right in this situation is right on. Normally one does not see menstrual type of bleeding
after sexual intercourse. So if this occurs on a regular basis, then you should have this follow up either with a primary care provider or a gynecologist. The first question one needs to figure out is whether you have a bleeding disorder, or just easy bruising? If that is negative then one needs investigate further to ensure that you don't have anything serious hidden.
Further, if you have not had a GYN exam recently then that should be scheduled. Certainly cervical cancer is the most important disease to rule out so if you have not had a gyn exam, that is something that you should get done. THe exam is uncomfortable but should not "hurt".
Things that you should ask your OBGYN or family doctor
include a GYN exam, brush biopsy
sample of the cervix for culture and cytology. Obviously the more common etiology includes cervical cancer, chlamydia, gonorrhea, trichomoniasis, vaginitis, cervical polyps for example. It is important to get the exam soon because most these conditions are treatable, often curable, even cervical cancer when detected early.