Supreme Court has made need the sole exam through which medical admissions are done. So you don't need to apply and sit for any other exam other than Neet for admission into medical colleges. But each state has its own independent counselling authority. So so you should definitely login to their website and apply for the counselling procedure you would be allotted a seat from the state authority.

No so you should definitely use a college predictor tool to know about your best chances in all medical colleges all over India. Here is the link

https://medicine.careers360.com/neet-college-predictor