I'm allergic to egg myself - I honestly find it hard to find really good egg-free baking recipes!
I've never really bothered much with egg-free baking until recently. I've made a few things like banana bread and a vegan white cake, but they haven't been 'wow, I have to make this again'.
OP, I've found Pinterest is a pretty good source for recipes.
This picture may help you too with egg substitutions: