Don’t go the throw up route, its bad for you physically and mentally.
About fasting and your parents, try the “I don’t eat before noon or after 6 pm” routine until they become use to your routine then try for longer periods like 24 hr. (adjust those hours to what you can do and stick to it)
And also you may find intermittent fasting works well for you.
I let my family know that I only eat between certain times in the day. I still sit with them at dinner but I dont eat.
If you want to do longer fasts, let your parents watch you make a plate for yourself to save for tomorrow or something and let them know that dinner is outside of your eating period.
If they’re pressuring you to eat still, I think they could be satisfied if your have an apple (for me, I eat clementines) and a glass of water. There are healthier options for you to eat and still be full.
Lately it’s been an issue with my family to so I’ve been looking into OMAD that I have with my family. Usually, parents are more upset that you dont eat with them bc eating is such a social activity or whatever.