I've used Earplanes the last three times I've flown, and had no problems with them. I really like them, and hope to never fly without them ever again!!!
At first, I was going to say that I couldn't see anyway these could cause stomach problems, but then I remembered my recent experience with a hearing aide fitting. When the hearing aide was inserted into my ear, I had a coughing fit. The audiologist said that happens with some people, putting something in the ear can trigger a cough. Sometimes coughing can trigger my gag reflex, causing me to vomit. So, just a guess on my part, but maybe this is what happend with the child. I've never had a problem with them, and my daughter didn't either the one time she used them.