What can I use as an egg substitute? (Severe allergy in my house mate)

You can definitely skip the egg or use bread and milk as Susan suggests. Another option (used often for vegetarian or vegan meatballs) is a little cornstarch mixed with water.

You can use bread and milk, but the recipe already has a large amount of breadcrumbs. Some people use ground flax seed mixed with water. They very well could be fine without the egg. I know people who never use them and their meatballs are always very tender.