B.Arch

Yes, you have the chance to get admission in Integral University through lateral admission process (for the 2nd year) for this you should not have any carryovers in the previous years.
Visit the website iul.ac.in for more information.
If you wish to get admission then hurry up because the classes have already started.

Eligibility for the Bachelor of Architecture (B.Arch):
The duration of the course is 5 years and to get admission into B.Arch. The student must be fulfilled the following conditions:
10+2 or equivalent with a minimum of 50% marks along with the compulsory subject of mathematics.
10+3 years Diploma in any stream from a recognized university/ board/ institution.
Cleared NATA (National Aptitude Test in Architecture) with the 80% marks conducted by Council of Architecture.

Here are the subjects of B.Arch:
1. Architecture design
2. Building construction
3. Theory of design
4. History of Architecture
5. Building science
6. Building management
7. Architectural drawing
8. Computer and software lab
9. Workshop practice
10. Architectural appreciation
11. Theory of settlement

Here are the top 5 architecture colleges of India:
1. Sir JJ college of Architecture, Mumbai
2. SPA, Delhi
3. CEPT university , Ahemdabad
4. Chandigarh college of Architecture
5. IIT Roorkee

NIT-Bhopal (MANIT) is an excellent choice for pursuing B.Arch. Please refer to the link provided below for details regarding placements, admission criteria, fee structure etc. from MANIT.
Link: https://www.shiksha.com/college/maulana-azad-national-institute-of-technology-bhopal-36786.

You can apply for any college in India through outside counselling.

To take admission in JJ College, you have to score above 150 marks out of 200 (open category) in NATA.

What is your score?

Unfortunately, you can't. National Institute of Technology accepts only JEE Mains paper 2 rank to admit students in B.Arch. IITs accept NATA score. However, there are some other colleges which accept NATA score.
Hope it helped.

True that even with self-study, you can achieve anything. In this case, clear the JEE Mains, but that doesn't mean it is the easier of the two alternatives. Coaching makes life easier for its students, and contrary to the popular opinion it does not have to be a nightmarish experience. And it will definitely improve your rank.