Congratulations on Qualifying NEET.

I believe having a score of 420 , in spite of having Category Advantage you might have bleak chances in securing a seat at any Good Government or State Medical College in J&K or anywhere in India. Of course if you do have monetary resources you make make into one of the private Medical Institutes or maybe into a Government Dental College in BDS, provided you are interested. Do keep a check on the State and Government counselling procedure and dates.

However my personal suggestion to you would be to consider a drop. It is hardly 6 more months before NEET 2021 is conducted in April/May next year subject to COVID conditions. Most of my peers securing in 400-450 range in first try, secured atleast in the 550-600 Range next year which increases your chances in securing a Government Medical College.