I don't want to go against your doctor's advice, but I'll share our story regarding Dylan's egg allergy as it seems quite similar to yours. It's a long story so I'll condense it
We've known Dylan was allergic to dairy since 5.5 months. We got an allergist's referral around 16mo after several mystery reactions and wanted to know what was going on. His blood results were surprising - he gets hives on contact with dairy, but those levels were his lowest. His levels were twice as high for eggs! I was stunned, because he had eaten egg white pasta multiple times with no problems. However, contact with actual eggs causes instant swelling and hives. The way my allergist explained it, Dylan is allergic to eggs in their natural state (so if you have to crack an egg to make it, it's unsafe) but eggs in processed foods seem to be ok.
I'm still quite careful because of the severity of Dylan's reactions, and TBH he can't eat many processed foods anyway because of his other allergies, but I continue to serve pastas and the like that he's had safely in the past.
Hth