I'm having somewhat of the same problem, though I do (...or did) love eggs. I'm on day 8 and can't imagine eating this much meat for the remaining 22 days...
I was raised vegetarian and didn't eat meat until 32 yrs old (4 yrs ago). I started when I was pregnant and morning sickness had turned me off from off most of the protein-dense vegetarian foods (eggs, dairy, beans, soy, etc). Before Whole30, I was eating meat maybe once a week, sometimes going a month or more without it.
The past week, I've eaten eggs for 2 meals and meat for 1 meal every day. I used to love eggs. I'm starting to dread them though. Same with the meat. I can't stand fish but I'm thinking of trying a few milder ones just to add some variety.
This is my second elimination style diet and both had me relying on eggs and meat for protein. The way I got through it before was to pick something tolerable and then eat that all the time with minor changes until I was truly and thoroughly sick of it. Example: plain scrambled eggs, scrambled eggs with spinach, scrambled eggs with herbs, scrambled eggs with curry powder (super awesome!), scrambled eggs with spinach and curry powder. Ok, now I'm sick of scrambled eggs. I'm going to make deviled eggs with various fillings until I get sick of that. By the time I did a few variations of this, all I wanted was plain scrambled eggs again. Pick your least objectionable animal protein. Perhaps it's boneless, skinless chicken breast. Start by just brining and roasting it. Keep eating that until you hate it. Next meal cook it in a skillet and make a pan sauce. Keep eating that until you hate it (there are endless pan sauces to be tried though!). Now try slow cooker pulled chicken. How about spicy indian chicken curry? Thai coconut chicken soup? This sort of thing got me through and honestly made me a better cook when it comes to meat (something I didn't have any instruction on growing up!). And maybe eating chicken every day will make you want to switch to beef or pork or more eggs.
(this may not be an issue for you, but like the article linked above, I also have to get all my meat from ethically raised animals. We have our own chickens and ducks for eggs and I buy all of my meat directly from local farmers - at their farm where I can see how the animals are raised.) Good luck!