Right off the bat - too many processed carbs, no protein whatsoever...little or no fiber...and WAY too much sugar.
If you want to burn fat - ya need to eat a bit cleaner than that. BTW yogurt also has quite a bit of sugar in it. And you REALLY need to add protein. I checked your profile and you're still growing, hon - you need to eat more than just sugar! Sugar is going to spike your blood level and you'll end up hungrier than ever and craving even more sugar.
So your mom won't cook - then you need to take some initiative and cook your own stuff. I'd suggest investing in a George Foreman Grill - I've seen the "Champ" version for less than $20 at Target - and you can cook fish, chicken, and even some lean beef on it with little muss and fuss.
Instead of Frosted Shredded Wheat and Rice Chex - try eating oatmeal (NOT the instant stuff in the envelopes - get the old-fashioned kind), potatoes (both 'white' and 'yams/sweet'), brown rice, etc.
Fruit juice is all sugar - you're better off eating whole fruit - though in moderation.
Especially since you're lifting weights...PROTEIN is so important. If you're not eating enough protein, you are sabotaging your efforts - if you aren't feeding your bod enough protein, it will start burning MUSCLE and not fat!
I would like to suggest reading "Body for Life" by Bill Phillips - it's an uncomplicated eating and workout plan (check your local library)...and feel free to drop in on the Body For Life/Bodybuilding thread here at 3FC for more ideas and tips...
Another great website to check out is Krista's at
http://www.stumptuous.com/weights.html - it's geared towards women and has plenty of no-BS info.
It's great that a young person like yourself is trying to take control of her body...now all you need is the KNOWLEDGE along with the proper mindset and determination...you can do it!
Take care!