I feel you, Katie! My son turned out to have food intolerances, not allergies, but we've also been through the elimination diet and lots of investigations early on.
One thing I was told and that you didn't mention is that children with food allergies might also be more prone to catching colds. It's like they have a sensitivity to the upper respiratory tract. My little guy had his first cold at 6 weeks old and plenty of bronchiolitis episodes until he turned two.