B.Tech Scope

You can go for automotive designing.
Automotive Designers
- Are involved in designing vehicles for mass production using both their design and engineering skills
- Research for new ideas in automobile design to develop a new vehicle design or bring about modifications in the existing design
- Use their creativity, art and engineering skills, to make designs which meet safety regulations, are functional, attractive, and comfortable
- Prepare 3D designs with details of shape and color using
- Computer aided design software. Construct a mock up or scale model of their designed vehicle, using clay
- Make a presentation to the production team and the management giving all details of interior and exterior design of the automobile, colors and materials
- Follow the production process and marketing to track the success of their design
https://www.shiksha.com/careers/automotive-designer-223

Yes, there is a good scope for B.Tech even if you study in a private university. Actually, private universities provide a better way to study and they will also be good for placements and exposure. (Not all private colleges). They will be better than some government colleges (not IITs and NITs).
The only thing is the fee structure they have their right to charge that amount.
But if you plan to get into a private university, then verify the factors like placements, faculty, accreditation and rankings.
Go for top private universities like BITS Pilani, VIT, SRM University, Manipal University, SASTRA University, Amrita University, Amity, etc.