Hi Ananya,
I started at ITP last year. NYU is expensive so you should really think long and hard before committing to such substantial debt. I was lucky enough to get a scholarship at ITP but I still have to take out loans, not to mention am paying for undergrad loans. The program itself is something I've never experienced before. It's equal parts mad scientist laboratory and tech startup. The greatest thing about ITP is your peers. Each class is 100+ people from all different types of backgrounds. Your classmates and the things you learn from them are arguably more important than the classes you take. As far as NYU goes I haven't really taken advantage of their "network" nor have I at ITP; however, there are companies coming in weekly to look for students to hire and demo their new warez.
Your background is not a problem at all. We have photographers, painters, dancers, lawyers, engineers, people from all backgrounds.
Hope that helps.
Ask if you have more questions.