Hi,
You dont have register separately for neet and bams counselling , register for neet counselling and fill your choices and preferances of the colleges which you feel that you have a chance to get admission , you can also choose bams colleges in preferances .
You can also click on the college predictor link mentioned below to find a suitable college https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer