Hello, 

Yes, you should go for private colleges under up state quota counselling with your OBC certificate. But the chances are not very bright  and in the 2nd round ir the mop6up round you can expect of getting a private medical college. Again i am saying that the chnces are not so good, but some chnces are there. May your luck favours and you bag a bams seat in a good private colleges of up. 

Hope this helped. 

Good luck!