Unfortunately an egg does a lot of damage. You'll find that it may have put a dent in your door but the paint surface is also affected and a polish won't remove the evidence. When the egg hits the surface the shell breaks into tiny pieces and actually break the surface of the paint a little, then the yoke does the rest.
It's acidic and then starts to etch the surface of the paint work and where the shell has impacted it'll have damaged it so the yoke will then start to eat away at the damaged area quicker than the undamaged area. If you leave it long enough it'll actually eat all the paint away down to bare metal. :o
By the look of the pics you may need to see a panel beater to get the paint work fixed and remove the dent if it has one. :(