I would not re-introduce it without seeking medical advice, in case this is an allergy and the reaction is worse each time.

If it were me I would speak to a doctor or baby health nurse to get some advice.

Some people are allergic to eggs and they can make them seriously ill. It is better that they vomit it up because in really bad cases the airway can become swollen or they can have breathing problems the same as people with asthma. People with egg allergies can’t have flu vaccines because they have egg in them. Another thing to consider too, is the fact that egg is very high in protein. You may be doing your baby a huge favour by not giving her eggs until she is older. If she vomits up again in 6 months or so you can be pretty sure that she is allergic to them.The baby’s kidneys may not be mature enough to cope with too much. The daughter of one of the girls I worked with never objected to eating egg custard she was given. It was only when she vomitted it up a few times that she realised she may be allergic to eggs, and that proved to be the case. My brother, even as an adult gets hayfever if he has more than two a week. Mum had to take him to an allergist to find out what foods he is allergic to when he was 5 years old. He is allergic to several foods, some more than others; also to various pollens from grasses and other foliage. One of the worst things is wattle blossom. A good part of the year he had chronic hayfever because of grasses and bushes in the school yard. We had to go past the local golf course which was surrounded by wattle and bottle brush bushes to get to school too.
Mum was told he may later become asthmatic but so far he hasn’t.

I haven’t had my daughter vomit when given/ eating a food. I have had problems with her eating eggs – I tried scrambled, hard boiled, frittata, and omelette but it wasn’t until I tried French Toast that she actually ate it. She will now sometimes eat frittata and also a thin, plain omelette.

Is she allergic? Has she had any other reaction to the eggs other than vomiting? I keep trying periodically (every couple of weeks) with the foods she rejects. Sometimes she’ll try them again, other times she just outright rejects them without trying. It’s really quite soul destroying.