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The only problem is, my brother and sister eat the junk food as well, and my mom has no intent on stopping buying it because of them.

I've tried to ask her to start buying healthier snacks and she has gotten some... Though nothing that's tremendously going to help me.

Well set up a little program for yourself. This is what I do.
For every "unhealthy" snack or meal I eat. I try to find find out how many calories it has and for every 10 calories it has I do 1 push-up and 2-sit-ups.
I know it may sound a little intense but you can play with the ratio.

I know people love junk food because it's fast, quick, and tastes great, but there is a line you have to draw somewhere. Good luck