Hello there, if you look up the fact that the marks required to expect a seat in a government college. especially, you have to score atleast 480-500 plus marks, as you mentioned you belong to OBC category even considering that criteria it won't make much of a difference. So the chances seems negligible, probably you can get a seat till mop up round in some private college. If you can afford that, and I am saying this since the competition to take a seat in private college has increased so far lately. 

Hello,
As you mentioned with obc category and 387 marks, your chances of getting a decent government college in your state through state quota(85%) are quite high.
As the admission to medical colleges based on NEET is given under All India Quota(15%) and state quota(85%).
Some of the colleges you might get-

• Mysore Medical College, Mysore-previous cut off-378 marks
• Hassan Institute of Medical Sciences, Hassan-378
• Vijayanagar Institute of Medical Sciences, Bellary-374

Follow this link to better predict your college-
https://medicine.careers360.com/articles/neet-college-predictor/amp
Good luck

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