Firstly, you should think that every year there is a good number of student who crack the examination from Tamil Nadu. SO you mustn't be very tensed about it just you need to strategise the study plan by yourself.

Now for most board the curriculum is mostly the same. So the things you will learn in the NEET preparation will help you in your boards as well and the things you will learn for boards will help you in the NEET preparation as well. See this are complementary to each other. Now I can understand your confusion that for NEET you have to follow the NCERT and for boards you have to follow some books else. But think if you want to learn the mechanism of heart, then will the function be described in two books be different?. As you can know, the knowledge is definite but there are changes in language but the concept is the same. Now a possible strategy for you can be, read the topics from the NCERT and just revise them from your state board books. This will help you to get the information which are not in NCERT but in your board books and the vice versa. This may sound a bit lengthy but if you start implementing it, then you will find it very beneficial.

To know more about the NEET preparation strategy visit the link below:

https://medicine.careers360.com/articles/neet-preparation-tips

I hope this answer helps. All the very best for your future endeavors!