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I am sorry to hear you are worried about Alex. My name is Rebecca. I am a veterinarian and will do my best to help.
If you look at his gums, are they a normal bright pink or do they seem pale? Was the egg fresh, or old and possibly rotten? There are infections, like Salmonella, that can be passed in birds' eggs. He may need to be on antibiotics if he got an infection from the egg.
Until you can see a veterinarian, you can try probiotics (Fortiflora, Proviable from pet stores or Culturelle from a drug store), and you could give him some Pepto Bismal (1/2 to 1 Tablespoon once to twice daily) or Imodium (1 to 2 tablets twice daily) for diarrhea.
If his gums appear pale to you, this could be serious and he should see a veterinarian soon.
Let me know what other questions I can answer and if this was helpful!
I hope you were able to see my response; I have not heard back from you! How is Alex doing? Was this helpful; did I answer all your questions?