Thanks for posting your query.
From your description it seems that your daughter its getting urticaria
. Its a condition where there are red raised lesions on the body. There can be linear lessons like how you describe and is known as dermatographism.
The second possibility is a viral infection or a drug induced rash
I would recommend that you visit your dermatologist
and let him have a look and give his opinion.
The best treatment for urticaria would be taking anti allergic medications like hydroxyzine
. The dose depends on the weight of the child and you would require a prescription for it.
Application of calamine
lotion will be soothing.