I would definitely recommend going without eggs in your situation, but if/when you decide to go back on them, two things that you may find helpful are that whites are very hard to digest, (I usually don’t use them or if I do I practice a 1:3 ratio of whites to yolks) and the less you cook them, the easier they are to digest. Also, if you can avoid pairing them with other meats, starchy vegetables or grains and opt for lots of leafy greens you may find an easier time digesting them.
As far as protein alternatives, I’m not sure what the ‘strict diet’ is that you mention, so forgive if these are no-no’s but can you have quinoa, avocados, or grass-fed beef? I personally find rare beef much easier to digest than chicken.
I’m hoping you are finding the kefir helpful. A friend got me hooked on adding ground flax and chia seeds with nutmeg, carob powder, and cinnamon for a thick breakfast smoothie.