I think that you need, first, to tell what is the vegetarian diet that you ate and said it didn't work, and the diet your daughter is having.
There can be a diet of french fries and coke. There can be a diet of only salads. Etc.
I don't see why you would have felt ill and had headaches... unless your vegetarian diet wasn't well balanced at all.
As for the protein, there's at least as much protein in vegetable as there is in meat, so that just couldn't posibly be the reason. Unless, like I said, your diet and your daughter's are really unbalanced...
Vegetarians can eat eggs and dairy products. They're called lacto-ovo vegetarians. But if they eat chicken, they are NOT vegetarians.
Vegetarians who don't eat eggs nor dairy products, are called vegan.
Some people are "raw-foodists" and it mainly uncooked food (vegetarian). That is suppoused to be the best choice for your health, but I recognize I find it a little hard. Especially considering I live in Chile, and here we don't have any health food stores. Even though I haven't actually tried.
As for organic meat, I don't think it's ethically much better... after all, those animals were also killed.
Anyway, if you tell me more or less what is the vegetarian diet, I can tell you more. Any vegetarian diet should contain a certain amount of nuts.
By the way, you shouldn't give up just because once it didn't work My sister had tried a some years ago to go vegetarian as a New Year commitment, and she couldn't for long... but last New Year she tried again, and it really seems to be working now.
"You've never felt the rain, my friend, until you've felt it running down you back".