Hey Kunal - well you have some interesting elements but your profile is also very standard in many ways, and that 620 GMAT is, as you know, quite low. Glad to hear you're planning on retesting. We strongly encourage you to move your test date up though. You don't want to be writing essays and studying for the GMAT at the same time, and a Round 1 app will be important for you, given your demographic.
The other issue though is your GPA - if it's really equivalent to a 2.7 on the 4.0 scale then you're going to have a difficult time getting into a top school. This can be a dealbreaker, unfortunately, it's very tough to overcome.
We also would caution you against taking a job in a nonprofit just to boost your profile for your apps. That's not a strategy that often pays off unless everything lines up just so. In most cases we would say to stick with the current career but we obviously don't know the full story.
Sorry to be so negative about those issues! But they are real concerns and you'll need to work to mitigate them. There's lots of great MBA programs out there of course, and if you're flexible with your targets then your odds increase. We can't really suggest specific schools in this forum since we don't know enough about your needs and wants in an MBA (we do a more thorough discussion of schools and everything in our Comprehensive Profile Review which you can find on our site at essaysnark.com).
Hope that's enough to help you move forward with forming a strategy - without completely freaking you out!!!

If you have followups feel free to post them and we'll try to help you out.
EssaySnark