Hi AMemerWhoActuallyLovesSchool
You can also google a chart from a reputable medical site (websites ending with .edu, .org, & .gov, are ones most trustworthy) what is the healthy range of weight according to your age, sex, and height. With your findings you can show your parents.
If that does not work, see if your doctor can talk to your parents; have him/her tell them your health status and normal weight.
As to how to lose weight, yes avoid junk foods. but also avoid as much as possible processed meats such as ground beef, pork, hotdogs and sausages. Also avoid fried foods such as hamburgers and fried chicken. Finally, minimize consumption of foods with high carbs (carbohydrates) like buns used for hamburgers and hotdogs, Pizza crusts, etc./
Fiber is good but is rich in carbs, too much of it can make one gain weight. Here is a site you can read more on it ( https://www.webmd.com/diet/foods-high-in-carbs#1 ).
Finally, weight loss can be further lost through exercise. You can see Diet and Exercise as two wings being essential to accomplish flight.
Ideally, 20-30 minute a day is what is recommended. It doesn't have to be a high impact aerobics but walking 20-30 minute a day is sufficient. As long as your heart rate is raised by constant physical movements you will certainly lose weight.
I hope this helps.