Please hear me: YOU are in control of your body. Not your family.
Thus, it is YOUR responsibility to take care of YOUR body. Do NOT harm it buy making yourself throw up. It is a disorder called bulimia (which you already know, since you posted this in the anorexia & bulimia support forum, as well as the juice fasting forum). You can do serious damage to your body if you continue to make yourself vomit.
Food is NOT your enemy. I do not know your weight, but if you are overweight according to a scale (NOT what you see in the mirror - imagining yourself to be "fat" when in actuality you are not is called body dysmorphic disorder), then be patient with yourself. You will lose the weight, and keep it off because you did it in a healthy way. If you vomit to keep yourself thin or starve yourself, you will gain it back because that lifestyle is not maintainable.
Eliminate all processed foods, sugars and processed grains from your diet, if you are indeed overweight. Eats lots of vegetables, fruit, raw fruit/veggie juices, and protein like hemp, lentils, and chickpeas. You can include some brown/wild rice in your diet, and some buckwheat, quinoa, millet, and other whole, unprocessed grains. You can get these from a health food store and cook them as you would oatmeal. Eat raw fats, especially extra virgin coconut oil. Cold pressed flaxseed oil and extra virgin olive oil are also good fats.
Juice fasting is a great way to start a lifestyle change, if you are converting from a diet of unhealthy foods. But natural foods will nourish you. Do not fear these foods.
If your family is forcing you to eat unhealthy foods, just say no. It's YOUR body. There is no point in eating unhealthy foods and then throwing them up. If your family is concerned about your food intake, make/bring your own healthy foods so they can see that you are eating. Eat healthy foods and feel proud that you are nourishing your body so it can function optimally. Then you will look and feel healthy.
Exercise is important. Walk for an hour a day. The movement and the fresh air is good for your body, mind and soul.
Be patient. You will see results in mere months. It will be maintainable, and you will feel healthier.
You are the sole ruler of your world. Make the right choices FOR YOURSELF so you can thrive. Don't live by other's demands of you.
Take care of yourself and treat YOURSELF with the respect you deserve. You deserve to be healthy and be nourished by the right foods :)
Be patient and kind to yourself!! You are most definitely worthy of it.