Okay wow so here we are a few days later and this post has a lot of useful information in it! Here's what I've gathered so far:
It's probably not salmonella or a food borne illness in general because the symptoms take hours to set in.
Possible mild allergy or just intolerant to them.
Now here's where I've got a few more questions.
I looked up the symptoms of staph infection based food poisoning, and our symptoms sound A LOT like that, including the quick onset. None of my birds have any lesions, sores, cuts, or appear sick at all. They couldn't be carrying staph dormantly inside their bodies, then transferring it to the eggs right?
Another thing here that didn't even cross my mind until I was reading another post about this. We have eaten the eggs before in baked goods with no issues. I was not aware, but my boyfriend (who has had worse reactions than I) has eaten them in a few omelettes when we first started getting eggs. We have different work schedules so I wasn't aware he had eaten them before, in essentially the exact same state as scrambled, and he did not get sick from them. We changed our birds food since then to the Country Road (Rural King brand) Layer Crumble. Could there be something in that food making us sick? It's not spoiled or anything, and I was feeding them DuMor Layer Crumble before. Can't find ingredients online for either of course

But that is the biggest change I've noticed that could maybe make us sick now and not before.
Overall I plan to buy some egg wash and I'm going to switch their food back anyways because I haven't been impressed with the Country Road.