Hi M. :)
Listen to your gut. That would be my first bit of advice. Children speak to us in many different ways. If you are getting this dairy info, she may be sending you a message that your higher self is receiving. Never rationalize your instincts. Just go with them!
Now, I took my daughter off all dairy from the cow, anything with yeast, wheat, refined sugars, and dye. She was suffering from horrible eczema- scratching open itchy scabs... the head of her school thought she had MRSA at one point :\. She was diagnosed with asthma and she has allergies... severe ones to peanuts. IF your daughter has eczema, she may develop asthma and allergies as well, so just keep your eye out for that. I would have her allergy tested (when she's older- it hurts). With the asthma, my daughter never had an audible wheeze; she coughed a lot, so I thought she was always getting sick (I had no prior experience with asthma). So, getting back to your question about the eczema, in my changing the dairy, I replaced with rice products. Rice dream has milk- flavored, too. They have noodles... all kinds of things. It seems as if every other child these days has super sensitivities to what we grew up eating. I don't question it as the children that are being born these days are smarter and more in tune. Let us all as parents learn from them. If they can't eat certain foods, then know that they are bad for us. Too many children suffer from the same stuff nowadays. There has to be something to that. Your daughter also has to adjust to these foods, but 7 weeks seems like that would have happened already.
In response to treating the eczema question, I can help you with that if you would like to contact me personally. I have read every response I've seen about children suffering from this. There was one area of responses in particular that stood out and I tried it and it works! My daughter was just beginning to suffer the constant itching thing and I started treating her again and she hasn't complained since. This stuff is a God-send, especially since every medicine we tried did hardly anything except hurt her and burn. This stuff I've been using is natural and a blessing! If you would like more info, message me :) I would try this stuff first before anything the doctor gives. I've got a medicine cabinet filled with expensive creams that are worthless (from her ped as well as from dermatologists. I wish I knew about this stuff I now use, before, when all of this started with her. I would have saved tons of money and she wouldn't have been in all that pain and had all the irritation. Also, don't use Benadryl on the area constantly because that can permanently change the texture of her skin. The cortisone won't :).
I hope you find something soon that helps her. :)
All my best,
J.