• The NEET UG scores that you have mentioned above are a bit low to get you admission into govt. BUMS college. However, you do have chance to get admission into govt. aided or private colleges.
• Few non-Govt. BUMS colleges in UP are:

Hello dear student, 

As you said you have scored 251 marks so there is a probability that you get government aided College as you have category too . Otherwise getting government college is really very difficult with this less marks . I hope you understand that cut offs are really very high. I hope this was helpful to you

Best wishes