Erode

1. Government College Of Education For Women, Coimbatore.
2. Rvs College Of Education, Coimbatore.
3. Hindustan College Of Education, Coimbatore.
4. Sri Vasavi Educational College, Erode.
5. Rasama College Of Education.

Hello Rohit, Normally speaking admissions to all colleges perhaps with exception to deemed to be universities, is restricted to domiciles of Tamil Nadu. Hence I do not think you can get admission there. However I would advise you to speak to the college directly. They may have some ace up their sleeves! Best wishes.

As you would have a grip over mechanical topics, doing ME as a post bachelors programme leading to the professional degree which gives you a terminal Master's degree. If you are interested in updating technical skills, this would be a great option for sure.
Colleges in Coimbatore for ME:
Bannari Amman Institute of Technology
Velalar College Of Engineering And Technology

You should take CAT, XAT, SNAP, NMAT, MAT for taking an admission next year in any of the B-schools of India. For this you should start preparing now.