Why do I get sick whenever I eat breakfast?!

Why not cut out oil, caffeine and meat from your breakfast for the time being until you are ready to eat them as 1st meal of the day.
Try oats / cereals / fresh fruits / whole grain bread with peanut butter and eat slowly. You can try opening up your appetite by drinking honey lemon water with empty stomach (a small glass) then enjoy your breakfast at a moderately slow pace. A small portion is better than eating nothing or throwing out later.
It might be the rushing or stress that is making your body rejecting the food, so make yourself as relax as possible otherwise all muscles will be tensed up and will be difficult to consume anything.

That is a pretty heavy breakfast to eat for any day. Try having something that is not so big. Maybe have a bowl of cereal such as Special K, or something along those lines, change to skim, or at least lower fat milk, a piece of fresh fruit and maybe whole grain toast. If you want eggs, try them scrambled with some veggies tossed in, or boiled, but not fried in butter or grease. You could also go the unconventional route and have a sandwich with lean meat and veggies with mustard or lite mayo, or maybe some fresh veggies and fruit with a lite dip, those two I have quite often because I am not a big fan of the standard breakfast foods. A slice of left-over pizza is quite tasty for breakfast, just make sure it has less meat then veggies on it. Maybe you could have just a very light meal at home and then possibly have a bigger snack when you get a break at school or work (if you get breaks mid morning). Another thing you could try is having less to eat, but more times through the day. Some people benefit from having six smaller meals a day rather than the standard three big ones, depending on how your body processes the food into energy. Hope this helps you some, have a great day!! :)

Maybe you are pregnant.