Chennai

You can apply for TNEA exam, but you have to go to Tamil Nadu for giving this exam. Cutoff may be higher for other state candidates.

https://www.shiksha.com/mass-communication-media/journalism/colleges/colleges-Chennai
Refer this.

There is no good college which will provide direct admission and vice versa. So, as per norms, all good colleges have entrance exam as must for admissions and only then it is qualified.

It doesn't accept CMAT but only accepts CAT with 86 percentile and XAT with 80 percentile:
https://www.shiksha.com/mba/course/post-graduate-diploma-in-management-loyola-institute-of-business-administration-nungambakkam-Chennai-187300.

Please find below some good colleges to pursue B.Sc. Visual Communication in Chennai:
1. Asian Memorial College of Arts & Science
2. Chennai National College of Arts & Science
3. D. G. Vaishnav College
4. Dharmamurthi Rao Bahadur Calavala Cunnan Chettys Hindu College
5. Guru Nanak College.

Your profile seems decent.
For PGDM 2020 Intake, Great Lakes Institute of Management will accept scores of GMAT taken after 1st January 2018, CAT taken in 2018/2019, XAT taken in 2019/2020 or CMAT taken in 2019/2020.

Go and take admission in a law college and give the entrance.

DTU is the best option for lateral entry admission in B.Tech CSE based on university consistent ranking and track records in academics and campus placement.

Please go through the link:
https://www.shiksha.com/aviation/colleges/colleges-chennai