Heyy
With 14338 rank I think you might get govt medical college through state quota in up oy if you belong to reserved category. If you belong to general category then it will be difficult for you to get govt college in up. As per previous year cut off you might get following colleges Motilal Nehru medical college, lala Lajpat Rai memorial medical College, UP rural institute of medical sciences and research and many more.
Here is a link which has list of all the colleges of up with their previous year cut off
https://medicine.careers360.com/articles/neet-cutoff-up/amp
We are predicting this on the basis of previous year cut off trends. We. Are not sure about this year cut off as it changes every year depending on no.of candidates, no.of seats and difficulty of exam. So hope for better result this time.
Here is a tool which can predict college on the basis of neet score. I hope this might help you

https://medicine.careers360.com/neet-college-predictor?icn=NEET_clgpd&ici=NEET_article_view_sticky

 here I am attaching neet rank predictor tool

 please check out this link

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

Feel free to ask me in the comment box If you are having any further doubts

hope you find it helpful 

Good Luck!

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