Hey there, you have scored 396 marks in NEET and you are looking for colleges in Tamil Nadu and you also belong to MBC Category. Really that will be very helpful to you while taking admission in Government College as some special seats are being reserved for each and every special reserved category. Sorry to say but your marks are quite low for that but due to a lot of variation in the cutoffs this year there are fewer chances of yours for getting admission in a government college. I would rather suggest you see the government college's cutoffs and apply accordingly. 

I would rather suggest you check the colleges available for you at these marks at College Predictor at Careers 360 only and it will be very helpful for you while getting a seat there. It will be very helpful for you as it will show the best colleges available for you according to your category and even home state rank.

https://medicine.careers360.com/neet-college-predictor?icn=neet-clgpd_landing-page&ici=prediction-section_c360-home