First question, what do you eat that you are throwing up? I don’t really feel like eating after going 24, but I never throw up. I usually have a small snack, yogurt or something simple to digest and then an hour or 2 later eat a normal meal.
Your body might not like that you didn’t eat and I used to be really anorexic and the way I tried to get back into food of eating small amounts and slowly go back to meals. I would say don’t eat acidic foods like tomato’s and I prefer eating just bread or crackers for its dry and it will absorb some liquid in your stomach and make your body not throw up. And if you do, cooked rice helps too. I hope this helps.
Rule of thumb would be to only eat liquids for half the time that you fasted.
So if you fast for 24 hours, in the first 13 hours that you break your fast, you should stick with tea, coffee, smoothies/ shakes and soups.
If you’re having a hard time eating, slowly reintroduce food into your system by waiting another 24 hours to eat solids. If you’re sensitive to certain types of foods, avoid it.