Not a vegan/vegetarian, but the diet is mostly vegetables/fruit and only a little meat. Whether or not you are vegan/vegetarian, a good multivitamin can help you feel better. Imagine all of the vitamins and minerals you are not getting enough of.
Multivitamins have made me feel sick as well. A few of them had extra unneeded ingredients which could have made me sick like inactive ingredients, herbs, flowers and stimulants, and others made me sick because I didn't follow the directions, take with a meal, drink with a lot of water, and so on. They could also just be a low quality brand. Taking multivitamins isn't a requirement. It's sort of an enhancement, but not steroids like enhancement. I feel better taking them, but it's not a huge difference that I feel. I would say I have a little bit more energy and I get less sick as often.
Maybe if a kids multivitamin made you sick maybe you should talk to your doctor about it and ask them if they have any advice for what to get or if you can event take them? I've never heard of anyone not being able to take a multivitamin, except for the warnings on the back for people with high blood pressure, kidney or liver disease, or are allergic to yeast to not take their pill. Experimenting with different multivitamins and finding the right one for you might be good. Then again it may be doing bad?
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Don't you mind people grinnin' in your face