Hi thanks for your question.
Bleeding after sex could be due to many reason and cervicitis
is commonest cause.The lumpy big thing with blood which came out after sex could be a cervical polyp
which got avulsed during sex resulting in bleeding .The cervical polyp could be a cause for you pain cramps and bleeding.Yes other reason responsible for your symptom could be cervical cancer
I would suggest you to consult a gynaecologist who may be able to examine you to determine exact cause of pain,cramps and bleeding.
Hope this answers your question.