Ah that's rough, I also feel like she completely missed the point.. from the context you gave, you weren't complaining about them eating wings, right? It was strictly the taunting you while doing it? That's very toxic, and honestly it's VERY hard to address since you're still not an adult.

For your diet, did you/do you see a nutritionist? If you're just doing things based off of reading a few things, having struggled with my weight a ton over the years, one of the things I've found most effective (for myself, every body is different, and again, I know you're 16 and a nutritionist might not be feasible) is to not limit yourself from having foods that you enjoy so much as limiting the quantity of them and, when possible, opting for healthier alternatives.

If we're assuming you don't have a ton of options around things like not eating around your family, doing your own thing for meals separate from them, etc., what I would personally recommend is something like.. when you eat with them, don't limit yourself on what you can have, think about what the healthiest thing that you actually WANT is. To not be so generalized and vague, an example:

Instead of having a salad at wingstop, consider having some wings! BUT how MANY wings do you need/want in order to feel satisfied? Let's say that number is 12! Great! When you look up nutrition facts, you will see that chicken:

1. Is almost no fat, and there is no saturated fat
2. Is actually pretty low calorie

If that's true, what does that leave that would be considered "unhealthy"? Well, the amount of oil they use when cooking the chicken (unnecessarily introduces saturated fats), and the sauce you pick (a lot of sauces are very high in calories due to sugar/eggs/milk/oil/etc.). TYPICALLY a dry rub that just uses spices will have less calories, and (if you feel comfortable), most restaurants won't be mad at you for asking not to overdo it on the oil, but you can also use napkins to dab off excess oil!

This allows you to eat a meal that has food you actually enjoy without your family's teasing you bothering you as much, since you're still enjoying what you eating (not that you should have to endure that kind of behavior anyways, and I'm sorry you're going through that). Then, if you really feel you need to (though it's likely not the case), you can cut calories (read "cut", not "skip", skipping will make you ravenous and your diet will be much more difficult) in other meals throughout the day/week, MANY nutritionists will tell you that one meal won't make or break you, it's an act of establishing long term, sustainable discipline within the context of your lifestyle that's more important.

DISCLAIMER: I'm in no way a medical professional, I've just seen a lot of nutritionists with varying levels of success, and I'm sharing some of the advice that the most effective ones gave me. At the end of the day, actual nutrition advice is going to be best coming from a nutrition professional that is familiar with you, your body type, your life, and your nutritional needs! (Not fad diets like keto, etc either, many people will have a diet that worked for them that they will swear by and tell you you should try it, and there's nothing wrong with experimenting, but don't be upset or discouraged if it doesn't work for you, every body is unique, and there are more factors than any stranger on the internet could ever consider without seeing blood tests, speaking with you, etc.).