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.
Socks and shoes. I can’t find anything big enough for my clown feet at retail.