Your state category rank might be in the range of 9,000 to 10,000 or even higher. It cannot be exactly predicted this year as you might be knowing that the cutoff is expected to rise this year as the number of candidates had increased and also the paper level was called easy comparatively. 

But as per the last year's cutoff and this year's analysis I guess you have a fair chance to get an admission in many of the government MBBS colleges of Tamil Nadu provided you are an SC candidate.

1. Madras medical college,

2. Stanley medical college,

3. CMC ,

4. PSG institute of medical sciences,

5. Madurai Medical college,

6. Kilpauk Medical college,

7. Tirunelveli medical college,

8. Coimbatore medical college,

9. Kanya kumari medical college,

10. Govt. Vellore Medical college,

You can also refer the link below for additional information:-

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