Food labels must be thoroughly scrutinised for products containing egg or albumen. The emulsifier known as lecithin can be derived from egg, although in practice this is uncommon. If you in doubt about any product, it is best to contact the retailer or manufacturer. Others are allergic even to egg which has been well cooked. People who are fine with cooked egg are more likely to grow out of egg allergy.
Some supermarkets produce lists of their own-brand products free from egg.
Many people find these invaluable. The MMR injection is normally cultured on egg. Anaphylactic reactions to the MMR have been reported, but they are very rare. In any case, it's probable that in those instances, a component other than egg was responsible. If there are any concerns, the vaccination should be given to the child as an outpatient in a paediatric department with full resuscitation equipment available.