I am severely allergic to eggs so no annual flu shot for me but I have gotten multiple COVID shots without issue. I am a bit worried about a combo flu-covid shit in the future and will talk with my doctor about my options. I will say that it is possible to work with a physician or allergist and take half-shots of some vaccines. This is where you take half the shot in two spaced out doses to eventually get full coverage. I will admit that it didn’t work for me with the flu vaccine but it was definitely worth a try and the reaction I had wasn’t as bad as a full dose.