There is a different reason, eggs contain allergens and when having leaky gut the body is in a sort of confusion and attacks the large foodparticles that slips into the bloodstream cause it can't recognize them, not even that, your immune system creates antibodies which renders even eggs as "indecipherable" because of its allergenic legacy that results in allergenic reactions along with bloating/gases.
Best thing to do is just concentrate on the leaky gut first, heal it til the siuation stabilizes, skip taking good bacteries for a start til you know that they just don't sail away into your bloodstream and wreak havoc like pirates on a raid.
When you've established a more balanced state in the gut (you'll notice it) reintroduce the probiotics.
Just going through the amino acids, essential fats and onions and garlics is the best thing to do for the first weeks then after that just slowly escalating with probiotics and rotating anti-fungals to reduce the fungicidal inflammation so the gut lining can heal but continue with the leaky gut-regimen til you're absolutely sure you can tolerate eggs or yoghurt without any symptoms like itching in the hands/feets, gases etc. but even after that maintain a safe gutfriendly diet with whatever the gut environment needs to be safe til candida is being back in check.
The most important thing to do is to accept that the recovering will take a long time and just take the day as it comes since additional stress is not good for the metabolism.
Hope you have some found some good advices in my post.