M.Tech

You have a lot of options left with you as you have done you Masters. If you are very much interested in academics, then Ph.D is the obvious choice for you after completion of your M.Tech.
If not, then there are number of corporate giants that seek M.Tech pass outs as they want to hire subject matter experts. M.Tech makes you eligible for jobs in such big companies like google, Microsoft and more.

First of all, it does not matter how long you have taken to complete your B.Tech and IIT is a great choice if you pursue M.Tech from the same.

There are a lot of entrance exams for those who are going abroad.The exams are:
1. GRE
2. IELTS
After satisfying the eligibility criteria you have to show bank balance then only you are eligible.
Along with the bank balance, you must have a passport.
Instead of abroad, India also has good universities for M.Tech.

You need to take GRE and IELTS or TOEFL.

Hello Jhimi,
The following link below gives you the list of M.Tech aeronautical engineering colleges in Chennai:
https://www.shiksha.com/engineering/colleges/m-tech-aeronautical-engineering-colleges-chennai
However, Madras Institute of Technology is the best college for aeronautical engineering.