Yeah! You are eligible for the state colleges of J&K but you are ineligible for the 15% All India Quota as J&K doesn't keep seat reserves for other state students. Thus you can take admission in your state colleges but can't apply for any other state colleges.

In J&K there are in total 900MBBS seats and 200 BDS seats.

To know more about J&K MBBS admission you may visit the link below:

https://medicine.careers360.com/articles/j-k-mbbs-admission

I hope this answer helps. All the very best for your future endeavors!