Should I avoid eggs because of the cholesterol? What about egg whites?
Eggs are awesome sources of protein. It is ironic that the same people who promote eggs as being very high quality protein also ask that you throw out the yolk. The yolk actually contains much of that high quality protein and the egg becomes a poorer protein source when you throw it out! The right eggs (free range or grain fed) also contain healthy fats in the yolk, so your combination of a whole egg and an egg white is fantastic.
There are still some people who buy into the old myth that eggs are bad for cholesterol. This is due to some bad advice given in the 70s that has created sort of an urban myth. The reality is that, unless you have been diagnosed as someone specifically sensitive to cholesterol in food, you are fine.
Only a few people experience a raise in blood cholesterol through consuming cholesterol in foods - otherwise healthy individuals like myself can consume 1,000mg of cholesterol per day and still have normal blood cholesterol levels because the body simply stops producing as much of its own cholesterol.
When it comes down to it, eggs provide nutrients, healthy fats, and quality protein in both the yolk and the white. So it really just becomes a calorie consideration - obviously, if you are looking to reduce calories, you'll eat fewer eggs or make a combination of whole eggs and egg whites to reach your desired target.