Organic eggs have a much better nutritional profile than regular ones too, since the hens are allowed to eat real food (grass, bugs etc) and get some exercise. They’re not exposed to dangerous pesticides and they taste a lot better too, so the increased price is kind of justified (it still hurts). Plus, you have the knowledge that the hens weren’t abused, if you’re into animal rights and all that. Free range would be the next choice, but they’re probably still contaminated with pesticides and antibiotics, so you’d really need to test to see if you get a reaction.
According to the cleanse protocol here, eggs are okay in moderation. If you feel yourself feeling faint or struggling to function, the protein/fat boost should really help. You need to be careful and your safety should take priority. Good luck getting through it anyway. It’s much easier after the first few weeks.