Hello

With 442 in NEET you must have got a rank around 113000. With this rank you can apply for Private MBBS or BDS colleges in AIQ counselling. You may also apply for Management quota seats in Karnataka state counselling. You may also wait for AYUSH Counselling to start.

As far as Bihar State Counselling is concerned, with your rank and assuming you to be from general  category you can get Lord Budha Koshi Medical College and Hospital, Saharsa,

Madhubani Medical College, Madhubani

Mithila Minority Dental College & Hospital

Sarjug Dental College & Hospital, Laheriasarai hence I would recommend you to sit for State Counselling incase you decide not to go for AIQ counselling.

The chances of getting CMC Vellore are not high as even though it is a private college it is highly reputed and prestigious and has high cutoffs.

You may use https://medicine.careers360.com/neet-college-predictor to know about your chances of getting admission there.