Mayonnaise can be upsetting. Since she has been fine until eating the sandwich, it sounds like that may be the culprit. After eating a lot of beef and deer, my dog isn't so keen on chicken (though he will eat it). I gave him chicken today and he looked at me like "hey, where's that good stuff?" It is normal for a dog to not want to eat for a day, maybe two, if they don't feel well. I think she should be OK fasting for a short time. Just make sure she has water.
Chicken is the cheapest and easiest meat for me to get. I saw a beef tongue in the store for over $30! I started raising some of my own animals for meat. Rabbit and duck are hard to find; rabbit can be expensive (around $7/lb). I have also been fortunate enough to meet a meat processor who was going to give me beef (for free). Since I want to keep the relationship going, I pay him something at pickup (which includes whatever he has leftover). There is no way I could get the amount of beef he gives me for that price at the store (it would easily be 3+ times more expensive).