CBSE 10th

Raunit, yes it is possible. But most of the Govt. Polytechnics are done with their entrance tests are in last stage of their admission process. Better would be you try for admission in some good private university where admission process is still on.
Another thing is better option for you would be to join dual Diploma B.Tech course where you save yourself of the pressure of entrance tests after Diploma course.
After doing a diploma you get direct admission in the second year of B.Tech. There are many universities in India that are offering you these dual Diploma- B.Tech courses. Some of them are also offering you scholarships based on your percentage in your previous qualification.
So, I feel instead of simply doing a diploma and then again starting with the search for a college/ university for B.Tech,it is better to take admission in a dual Diploma-B.Tech course.
Here are some of the universities, you can visit their websites for more details:
MVN University, NH-2, Delhi-Agra Highway (NCR), Haryana
Lovely Professional University, get Road, Phagwara, Punjab
Maharishi Markandeshwar Engineering College, Ambala, Haryana
Best of luck!

Yes, you can surely pursue a course program in Interior Design after 10th.
You can take a diploma course program.
Diploma courses:
-Diploma in Interior Design
-Diploma in Interior Design and Decoration
-Diploma in Interior Design and Display (Graduates)
-Diploma in Interior Design and Display (Professional)
-Advanced Diploma in Interior Design and Display
After this, you can opt for a degree course in Interior Design.
Employment Opportunities:
Commercial Interior Designer
Design Consultant
Exhibition Designer
Institutional Interior Designer
Lighting Designer
Residential Interior Designer
Interior decorators
Window display designers
Design Educator
Facility Manager
Theatre and set designers
Skills Required:
-Drawing aptitude
-Ability to work as part of a team
-Visual sensitivity
-Knowledge of textures, materials and trends
-Ability to deal with technical details
-Analytical mind