Can I vaccinate my child with Bexsero if they have a dairy allergy?

No, allergy to egg white and cow's milk protein (I guess you mean by "dairy") is not a contraindication to any of the vaccines, including Bexsero. Of course, it is worth informing the vaccinating doctor that the child is allergic. I would like to add that each office where the vaccine is administered is equipped with a set of drugs that can be given in the event of a strong allergic reaction (so-called anaphylactic shock). You should therefore have no cause for concern. Before vaccinating your child, it is worth reading the leaflet for Bexsero: https://www.gdziepolek.pl/produkty/10616/bexsero-iniekcja/ulotka