An allergist told you to keep feeding an allergen to get her over it? Wow. That's bizarre. We had a bad allergist once but not that bad.
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Her regular ped. should be able to order a celiac (and check for anemia as well).
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Is the six year old having hives too?
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It sounds like you've narrowed it to dairy for the baby. I'm sorry! If it helps my son didn't show signs until a bit older too and he did outgrow his dairy allergy in time.
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The most common cause of hives is actually viral. It's within the realm of possibility that you and the baby have viral hives. It does sound like there is a dairy issue too though.
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Allergy testing prior to two is often inaccurate. That may have been the issue or it may have been that you were dealing with an intolerance rather than allergy. You'd avoid either way. Generally negatives on allergy tests are (statistically) accurate but some kids test more accurately with either skin or blood. Either way though any allergist worth their salt would say that reactions trump test results. So you correctly pulled dairy for her.
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The older daughter--I sort of agree with the allergist that celiac/growth/stomach pain are sort of out if his/her expertise and you may need pediatric GI if you don't find the cause. If you have a cooperative pediatrician I can suggest another test if you can't narrow down the pain cause for her to food. But food and/or celiac seem the most likely culprits I agree.
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First, though, I would see if the pediatrician will run a celiac panel on her. You need that and she does have signs. It may be the only issue. Don't pull gluten until you get her tested. She has to be consuming for it to be accurate. If the pediatrician won't run (even if he/she will perhaps given the growth issues) you would want a pediatric GI and that's probably what the allergist meant by the children's hospital or maybe he was saying that a pediatric allergist would help? I've no clue!
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To figure out if my son's GI stuff was food related I put my son on a four day food rotation (he was six too) and then kept a food diary. Finally we figured out his food trigger and pulled it and he's not having the GI stuff now. He has documented food allergies but I suspect this one might be an intolerance instead/next time he gets allergy tests I'll have them run it to check. He won't be eating it though!