Since you have basic understanding of how cars are built and how they work, next thing you need to expertise to become a car designer is designing and modelling skills.
You can do Industrial Design and Transportation/Automobile Design courses after B.Tech. for better and strong career.
In India, National institute of Design(NID) offers Transportation & Automobile Design course for engineering and other technical/designing graduates. Industrial Design Centre(IDC), IIT Bombay offers Master of Design programme in Mobility and Vehicle Design. Some universities/colleges and private institutes like DSK ISD - Pune, DYP-DC also offer related courses.
Besides Catia, you can learn Autodesk Alias software for car designing.
Most of the automobile companies take services of designing companies and centres located abroad. Some international companies have set up design centres in India e.g. General Motors, Bangalore; Renault, Mumbai. There are some design studios in India working with automobile companies. For training and internship, you can apply to these centres and studios.