1) there is no reason to throw away the yolks. You're throwing away calories and protein! For someone on a budget who's trying to eat a decent number of calories, why on God's green earth would you do this?
I think you're pretty young, so I'll go easy on you, but quickly: the prevailing belief that egg yolks were bad because CHOLESTEROL! and FAT! is dead. Egg yolks are perfectly healthy (in fact, they're the most nutritious part of the egg!) and conventional wisdom is FINALLY catching up.
STOP THROWING AWAY THE YOLKS!
2) why not beef and pork? If the answer has something to do with fat or how unhealthy "red meat" is, just stop
Also: see my comment above about breasts vs wings. I can get chicken drumsticks at Whole Foods (a notoriously expensive place to buy meat) for $2.29 a pound, and sometimes they'll be on sale as little as $1.99 a pound.
Let go of the idea that "chicken breast" is the only meat because some article says you should be eating "lean meats." For one, that's dumb, and for two, if you're trying to eat cheap you just don't have that luxury anyway.
Wings, drumsticks, etc are MUCH cheaper by volume than breasts. Plus, you can save your bones and make delicious broth (every week I make a crock full of broth from all the lovely bones I have leftover).
3) also, if you can find an ethnic grocer or some other small shops near you, they might surprise you. I can buy a kilo bag of goat meat from this Greek guy across the street for $10. Still not cheap-eating but it's worth checking into similar options.