B.Com

Refer the following link:
https://www.shiksha.com/accounting-commerce/ranking/top-commerce-colleges-in-Delhi/ncr/97-2-0-10223-0

Yes, you can get admission as the minimum eligibility criteria for the same is pass in the 12th standard from recognized boards like CBSE/ISC/PUC or equivalent board.

You can consider following courses:
Masters in finance
Masters in commerce
Chartered financial analyst
Certified public accountant
Association of certified chartered accountant

ICAI has MoU with few colleges to get CA student's B.Com done with ease. Few colleges like JNU, IGNOU and some more. Even I have done it from IGNOU.

BBA can be said to be the most relevant courses in management. You can always opt for BBA. The courses of BBA honors and BBA are almost the same but that of B.Com is not same it is different. You can check the official courses and syllabus included in the same.

There are various institutes which provide you the MBA courses without CAT or MAT entrance exams. You can always apply for that. Please find out those colleges and apply for the admissions there so that you don't spoil a year. Your skills and abilities are more important than the entrance exams scores. So do apply for the same.