My daughter bleached her hair about four weeks ago and we had to rince it off very quickly because it burnt her scalp, most of her hair did bleach apart from some of her hair unerneath. Will it be OK now to just highlight her hair on top of the bleach or will it go wrong

I wouldn't until you've taken her to a reputable hair dressers for some professional advice.

It sounds like the one you used was to strong for her hair, especially if it was already coloured, I would advice extreme caution where bleach is concerned at the risk of further damage to her scalp.

Better to be safe than sorry.

my daughter bleached her hair about four weeks ago and we had to rince it off very quickly because it burnt her scalp, most of her hair did bleach apart from some of her hair unerneath. will it be ok now to just highlight her hair on top of the bleach or will it go wrong
By bleaching it you're taking out the pigment in her hair. Highlights do the same damage. It is normal for burning of the scalp to happen, especially if she has a sensitive scalp. Bleach is a timing process and if she hasn't died her hair too many times it can have its effect in a short amount of time. I would definitely go to a higher end salon and have them take care of it. The same thing happened to my sister and they fixed it for $60.00