Basically, yes. I would suggest posting over in the Fitness forum for good advice on a program. You definitely don't need a gym to get fit! While there's no way to target fat loss, you can absolutely improve muscle tone and get rid of that "skinny fat" - here's a great article to start you off: www.sparkpeople.com/resource/fitness_artic
I don't think you can do much of anything in two months. :) Flat bellies are more about body fat percentage, and both strength training and fat loss takes time. I think you should abandon the time-based goals, and focus on slow and steady progress. This isn't a race!