This is the first time I heard of using an egg. Apparently it is a decent temperary fix. When I was young my dad told me to put a teaspoon of ground black pepper in my radiator that was leaking pretty good. It fixed it and I drove it for a long time that way, never leaked again. This was an older style brass radiator, I don't know if black pepper will work as well on the newer plastic tanks.
For $200 you should be able to find a decent radiator for that car. There are a LOT of them out there. I bet if you shopped arounf you could even find an aluminum one for $200.