Soo, we had a similar issue going until my DD was probably 14-15 months old, and I'm not really sure what the problem was, but we took milk and wheat out of her diet (& mine) for a few weeks... there was an immediate improvement. I'm talking she had totally loose stools with undigested food in them one day, then clay color marble poops, horrific screaming, writhing, and blood another day. It was worst after she would drink plain milk. She wouldn't poop for days, then when she did it was awful, like rocks, and obviously really painful for her.
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Two or three days after we quit milk and wheat, she was having perfect, easy brown poops, everything completely digested.  I was also feeling better. (For a while one day I'd have gross diarrhea, then constipation... sorry if that's TMI, but I had no idea what was going on, I'd never had digestion problems before my daughter was born. Anyhow that's a possible intolerance symptom, I learned.)
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With my daughter I think part of the problem is that we needed more good yeasts and bacterias in our diet, otherwise we were having some troubles digesting certain kinds of food. We both took anti-yeast medicine when she was around 3 months old (I had diflucan, and she got the banana flavored stuff.. nystatin?) because drs thought we had thrush. It didn't occur to me that these medicine upset the balance as much as antibiotics.
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I don't know if we'll totally be able to go back to eating whatever we want, but maybe! Now that it's been about a month off (I switched to giving her bone broths to drink instead of a milk substitute...plus lots of pears!), I've tried kefir (good) and sourdough (not sure... ). So now she's trying her first kefir since I had a good reaction to it. Hopefully it will help her. If not, we'll back off and give her belly a little more time to grow and heal.
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Also have you tried belly massage for her? That seems to help keep stuff moving.
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My doctor also acted like constipation is totally normal, but TBH, I question that. If I give my daughter a certain kind of food and it constipates her, and then I take it away, and she is fine... that tells me to just stop giving it to her. So no more plain milk, that's for sure. We'd only been giving it to her to help her gain weight, but I don't think it was helping that either.
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Yogurt is good but I guess the bacteria don't colonize your stomach. Supposedly the bacteria and yeasts in homemade kefir do. I imagine probiotic capsules are similar?
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Anyhow, good luck! It totally sucks to see them in so much pain doing something that should be easy and normal.