Yes you can get admission in government medical colleges of your state since you belong to MBC category. 369 was the cutoff for MBC in Thanjavur Medical College, Thanjavur last year. Rajah Muthiah Medical College had cutoff 308 marks for the MBC category. 

Refer to our site for further detailed information.. 

https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu

Best wishes. Thank you.