However, some people with Candida have an intolerance for certain "sulfur foods" (meats, eggs, dairy, nuts, broccoli, and many more) because they have mercury poisoning.
Take virgin coconut oil or even some extra virgin olive oil, they're both fats. I doubt your face would swell. Did you try raw (organic) eggs? How about tallow (beef fat) from an organically raised cow?
I guess it's also possible that you're having a die off reaction, but puffy face usually means food intolerance.