I played badminton yesterday and after 10 minutes I was breathing heavily and ready to pass out. What are some ways I can get into shape before the end of the month?

You might want to see a doctor before you begin any excersie program.
I would suggest start with something less demanding like walking and build up slowly.

If you're "ready to pass out" after 10 minutes of badmitton, then the first thing you need to realize is that the level of "in shape" you achieve at the end of the month will be relatively insignificant as opposed to where you'd probably like it to be.

Training effect is our body's response to self-imposed challenges that we put upon it, and it takes time for those responses to generate. In one month, you simply won't have enough time to challenge the body enough, nor will it have enough time to adapt.

Give yourself 12-20 weeks as an exercise cycle, and then see how much better you feel.

You are not going to get into shape in 2 or 3 weeks, it will take months of exercise and properr diet. Start by a regular workout several times a week.

I also have to wonder, was this indoors or out? I know where I am the heat is in the triple digits, so you would really have to limit your time outside.