I've had very few problems with makeup, but I don't know that my egg allergy would be as much a factor for me as it might be for others with egg allergy. Off the top of my head, I can't think of any makeup I've used or heard of containing egg, though.
I've reacted to eyeliner twice (once in 8th grade, so I have no clue as to the brand) and more recently to Ulta. I don't know if the reaction was just me or if it was pn/tn related. I regularly use L'Oreal H.I.P. liner with no problems which is my favorite liner if all time. It stays on incredibly well with no smudging. Cover Girl and Revlon products have been fine for me. I have occasionally used Wet n Wild, also. At one time Clinique had products with peanut oil plus they are pricey, so I don't use them. Honestly, since nut oils are expensive, my gut says cheaper may be safer.