Hello 

I am here to help you with your query

As you belong to ST category you got good chances .

Yes you can get into NIT 's too.

As you come under other state category slight difference occurs in terms of getting seat on top most NIT's.

You can get in good NIT's for mechanical and EEE.

If you want to go top college then branch shouldn't matter 

If branch completely matters then go for any of the NIT you get .

Don't worry NIT warangal is the best u really can have a good chance there.

For more queries do comment below.

Good luck