T.C.
Hi there! Since it is around the lips and your daughter is 5 I am wondering if she is eating/drinking things that are acidic... spaghetti sauces and tomato based products, orange juice or any juice for that matter etc... cut out some of the acidic things and if she is drinking them have her drink them from a straw. See if that helps in the meantime. If my son was to eat tomato based products and get them on his cheek or hands etc he would break out and it would look like a huge dry patch of burnt dry skin. He can eat them but has to be super neat and no slurping in the spaghetti noodles! lol
Also, continue with the moisturizing lip balms but try one that is more hypoallergenic- I think the BEe one (not sure of the name) is or it is more natural anyhow. With the weather she is bound to be licking her lips more because of the dryness which will just worsen the problem.
Good luck and let us know what the allergist says! Blessings to you and yours!