This is a great post. +1 for potatoes and onions. (Just don’t store them together, they spoil each other faster)
One thing I’ll add is that if the OP is in the United States, commercially sold eggs have the bloom washed off them before they get to store shelves, so they MUST be refrigerated.
You can get dehydrated egg products that are shelf stable until you use them. They’re not perfect but for most purposes they’re good enough.
Hives are one of the clearest signs of an allergic reaction. There is basically no normal circumstance where those should occur.
It sounds like there are potentially other factors contributing to your symptoms at home, but the last couple of things happening with dogs in general strongly suggests that you have a dog allergy.
I have to echo other posters here and urge you to see a doctor about testing (if financially viable) and mitigation advice.