Can an egg allergy appear overnight?

My daughter was at my moms house. She had a cold (sore throat, coughing) that she was taking medicine for. My mom calls me and said that when she woke up from her nap she had all these red spots all over her body. So we went and took her to the ER. (I'm 5 months pregnant and was terrified it was chicken pox) So we see the DR and he says to give her benedryl its probably an allergic reaction to something. So we give her some the spots go away. Later that night before bed she asks for scrambled eggs to eat. I make them for her and she eats them, then falls esleep. Later around 3am I woke up because she was coughing (to give her medicine) and when I turned the lights on I noticed the same spots are back, and she is itching them like crazy in her sleep. I give her the medicine and they are gone by morning time when she wakes up. So the next day I am trying to think what could have made those come again, then it pops in my head the eggs- I wonder if my mom gave her some. Come to find out she did have scrambled eggs before her nap and earlier on in the morning. She has been eating eggs for 2 years atleast!!! is it possible to get an egg allergy overnight?