I want to get slimmer!?

Hi! Now before you go all, "You're young! Enjoy your childhood and stop worrying about your weight!" on me, please hear me out. Is there something wrong with trying to be healthier? Nopee! My extra fat is a sign of unhealthiness, so there: it's perfectly fine! My parents and mom call me fat allllll the time and it's really annoying. I'm 13 years old, 5 foot 3 (technically 5 foot 2 and 3/4 of an inch... but whatever), and my weight ranges from 98 to 103 pounds. So, yes, I'm a little hefty hahah. I don't do any sports or any form of exercise. So, I decided to start exercising on the machines we have down stairs. My diet is kinda weird. Like the food I eat isn't unhealthy like McDonald's and stuff, it's healthy(ish), I just eat A LOT! I probably eat about 1,700 calories per day. Hahahah. I eat pasta for 70% of my meals because I am a vegetarian and there's not a large selection of food I can eat. I make my own food, not my mom, so if my mom ever makes my food she will add in some fake meat and broccoli, too. But when I make my own food (95% of the time) it's just pasta or just rice. So I have been using the rowing machine (that machine where you slide backwards and pull the chain... that's what she said.) alternately with a treadmill for my once-a-day "workouts". I use the treadmill at a slow pace (15 min-20 min miles) for a mile, row for ten minutes, walk/run another slow mile, then row for 5 minutes. These exercise sessions last about 45 minutes and burn about 200 calories, plus they make me feel healthy and good! My thighs and stomach (and chin, but I don't think I can do anything about that) are the flabbiest areas. Is there anything I should be adding to these little workouts that can help? And is this pasta diet I have bad? Thanks a bunch, and please don't judge me on my age!