NEET score more of dependent on cut off and no of students has achieved that cutoff . According to your marks it is good upto now to get admission in private MBBS course in West Bengal. ( Though it depends on no of students from West Bengal has crossed the cutoff)
In MBBS you could get private college wait upto the completion of counseling. From the first round you are well enough to get to know your situation and problity of getting colleges.

Joint Entrance Examination (Main)

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National Eligibility cum Entrance Test

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