msg food allergy?

My 18 month old daughter has had several face swelling, severe hives/rash break outs after eating foods, but thankfully has never had any breathing issues.  After recording what she ate and a few times testing with our allergist, she has skin tested positive for eggs, tomato, garlic, and peas.  She also had positive rast test results for these foods as well as peanuts.  She has no issue with soy, wheat, or dairy.  She now seems to be getting a rash from parmesan cheese.  I did a search online since I thought parmesan cheese seemed an unusual thing to be reacting to and found it along with tomato and peas have a natural level of glutamate, so I'm wondering if that could be the connection between these foods she is allergic to?  I have seen discussions that you can have a msg intolerance but it is not an allergen, but I'm not sure if that refers just to the additive or the natural glutamate.