Stomach Problems in 1yr old

Treasure

So my daughter was breastfed for 1yr n 3 months. She never ate baby food well. When she stopped being breastfed we tried toddler formula, regular milk, almond milk, soy milk n she couldnt tolerate any of it. We tried adding strawberry n chocolate syrups, nothing. Her ped said just give it to her via other foods like putting it in scrambled eggs and cereal bars. Whenever she gets milk in her system she has severe diarrhea all day and sometimes would cry a lot. But its not lactose issue because she loves other dairy stuff like cheese n ice cream.

At about a year n half we noticed something weird with her belly button. ped said she has a small hole not quite a hernia n that generally it will heal itself but could require surgery later in life if it doesnt. Her belly looks funny to me like its unusually distended (picture below)

On top of that and the milk thing she never really ate well. she nibbles and says done. we were really concerned about her eating. from time to time she’ll eat well. Her ped says she wont starve herself n will eat when she’s hungry. Well recently shes been puking after those times she eats well. not huge amounts but kind of like spit up after burping a baby to give u an idea of quantity.

I really feel like it’s something wrong with her digestive system but scared to keep questioning n seeing doctors. shes been to ER like 10 times for unrelated issues like falls, ear infections, n high fevers. So im afraid this issue may make them think i have munchausen syndrome by proxy. Her father is concerned to but he is military and away so im the only one taking her to doctor. Any suggestions? I really feel in my gut something isnt right