Eggs do have much protein in them, though not as much as the other things that you did mention.
The main issue with eggs is that have much negative effects as they do positive -such as colestirol levels and so forth- and because of these, most people tend to shy away from them.
The most favoured uses of eggs are as Egg White Omletts for breakfast (cooked in very basic form of oil) or as a binder for other meals.

Personally, I's find eggs to be of great value -if used sparsely, twice or thrice a week at most- for they are inexpensive, plentiful and malible.

Though, in ways of diet, I's tend to take the very Martial Artists appraoch of my's Sifu and eat everything that I's desire -as long as it is not too unhealthy, artificial or repugnant to my's stomach.
Needless to say, I's have eaten many a strange thing in my's life.

Peace
The Pimp NeonBlack

Oy.  Newbie here.

In any case, I like egg whites, primarily because I have to cook my own meat and fish is not an option in a Hindu household.  Also, considering my current location, sashimi is out of the question.  So, I've had to constrict my lean protein sources to lean meats and Egg Beaters; which, by the by, are basically yellow-colored egg whites in a carton.  I've been losing steady poundage of body fat since I used it to fill out my food while cutting out the heavily refined portions of the meal.

I guess I'd like to say that egg whites are good fillers, and the occasional bit of yolk is acceptable (usually one yolk per six eggs).  However, when it's used alone, be wary of the yolk because most of the lipid content (if not all of it) is concentrated there.

Hhmmm. . . If you're body rejects certain fats and oils and almost all processed and artificial foods, The Pimp would then recommend switching to a more vegatable based diet with high ammounts of legums (beans and such) and nuts (mainly cashews, walnuts and almonds).
Try a more Asian (Chinese & Thai mainly) style of meals with vegatables and nuts stirred fried in a light oil -peanut, grapeseed or linseed- with a good dose of natural seasonings spread through (mainly natural and freshly ground spices).
Being of Cajun blood, such things should be natural to your cooking sense and platte.

Also, American Ground Beef is majority off cuts and fat. Even if you do good and drain the 'meat' well, you are style prone to same rejection syndrome as if you ate full fat and bad oils.

After briefly viewing your history on these threads, I's would highly recommending getting your metatabolism rebalanced as well as finding a means and method of controlling your blood sugers and glucose levels -as they to effect what you can eat, when and your overall metabolic rate and system.
Then you can worry about your total diet and all things that follows.

That is the only advice The Pimp can give at this point in Existence.

Peace
The Pimp NeonBlack

If you are having issues with your insulin levels, than you may actually have problems with you pancreus. This is a common side effect of chemotheropy and, if untreated, can casual many long lasting issues.
A bad pancreus would also replain you reactions to fats and oils as well as some of the other problems that you mentioned.
If you haven't already sone so, I's would highly recommend speaking to your doctor about this during you next appointment.

As for fresh foods: best to seek out a farmers' market or Co-op market.
They often have very excellent and fresh produce for very little money.
The only issue is finding such things in your local area.

Peace
The Pimp NeonBlack