Hello,
As you have not mentioned, I assume you belong to unreserved category.
As you know admission to government medical colleges is based on NEET marks is done under two categories-All India quota(15%) and state quota(85%).
With 360 marks in UR category , you might not get any government college through All India quota or state quota. You might not even get private colleges.
So I'll suggest you to go for some other courses or prepare fo NEET next year and secure better marks.

For more follow thus link-
https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu/amp

Good luck

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