Hey.

The cut off for admission in government colleges in Tamil Nadu under the State quota for the general category in 2019 has not been reselased as of yet

But in previous year 2018 was a rank of 1971 state rank and  a score of 370 marks. The cut off changes each year due to several factors like level of difficulty or level of Competition etc. This year as the paper was easier the cut off based on marks will be higher than before. Considering your rank, and the previous year last rank you seem to have a fair chance of Admission here. You can use the link below for more details.

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

Best of luck