Yes it(and many other things) is possible. If you are having bleeding with intercourse, you should DEFINATELY schedule a visit with your GYN. There are a multitude of reasons this could be happening. Some could be serious but others are an easy fix. Get it diagnosed properly by a qualified professional for best results.
As to the penis hitting the cervix during intercourse, it isn't impossible but it is unlikely as our bodies are designed for this not to happen.
Women who HAVE experienced this have almost without exception described the experience as exquisitely painful.
Bottom line: See your GYN and get diagnosed. After you do, your sexual life should get better! You won't be worried anymore so you'll be able to relax and enjoy.
Sorry I can't give you any magic solution. I wish you the best.
I have experienced this myself. I was having intercourse with a partner who had a large penis & when he was entering from behind I could feel him hitting my cervix. Other positions were no problem so it was obvious that particular angles caused the issue. It was painful & caused bleeding. For the next couple of days I had cramping.