Hello Aspirant,

Hope you are doing well!

Sorry Dear,getting a medical seat in Tamil Nadu with a score of 314 is really difficult,as  the minimum required score is  350 both in government and private colleges,But,yes you can get seats in few colleges through Management quota,but that might be costly for you.

For More Reference I am providing you with the link of all the colleges of Tamil Nadu,along with their Cutoff score:

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

Also,To find all the possible colleges under your NEET rank,you may go on the link below:

Hope This was helpful!

All the best!

Keep Smiling :)