https://www.careers360.com/courses/graphic-designing-course .

Above I have attached a link below that contains detailed information on how to choose graphic designing as your career option .

You should refer to that link as it will help you in widening you thoughts and will help you to take steps towards your dream career.

There is no specific bTech degree that teaches graphic designing solely. The course of graphic designing do involves computer but that doesn't means you have to go for computer engineering.

You should go for Graphic designing courses directly if you are interested in that. Why to waste your time on BTech degree.

Although you can also go for graphic designing in your master degree.

Refer to that link above and I feel it will solve your major confusions.

Hope that helps.

Thank you.