egg allergy?- possibly TMI and long

After yesterday's weight gain thread I decided to help Luke out with some egg and cheese for breakfast. I know it's dumb of me not to introduce them separately but I didn't.
He has had egg yolk once and a little shredded cheese before but he ate more this time and I gave him the whole scrambled egg.

His face got red after eating it but he has eczema and we didn't put lotion on him last night so that could be related to the egg or not.

He cried before his nap then finally fell asleep. I was laying next to him and he started vomiting a lot. Everywhere the vomit got ended up being splotchy red (his neck and back of head) and he was scratching his face (he does that with eczema sometimes too). I just gave him some antihisthamine (RX from dermatologist) to help with the itching and he's sleeping again (I'm laying with him to keep an eye on his breathing and vomiting)

I'm going to hold off on eggs again for a little but is this how your egg allergy showed up?