Will egg white make me healthier?

the egg white is made up completely differently to the yolk and it is considered as mostly protein, where the yolk is very fatty. the problem with egg whites is they can be too protein rich. if you eat loads then do some exercises to acquire some muscle :)

yes the egg white is the healthiest part of the egg

Yes, eggs white is low in calories and has a lot of proteins. All the cholesterol thingies are in yolks.

I would strongly suggest you study the egg as a whole more closely as it is one of the best foods you can egg for your body and I can't accept the fact you have to stop eating the yolks, unless you are on strict Doctors orders.
Latest results say we can eat one whole egg per day.

Egg Nutrition: Yolk vs. White
Egg yolks are indeed full of cholesterol. Like most cholesterol-rich foods, they are jam-packed full of important nutrients, especially the fat-soluble vitamins and essential fatty acids.

In fact, the slew of nutrients in an egg yolk is so comprehensive that a few a day would offer better insurance than a multi-vitamin. Most importantly, the yolk contains most of the nutrients in an egg.

Egg whites, on the other hand, contain far fewer nutrients. The only thing that could justify their consumption is their attachment to their companion yolk.

Don't believe it? Below is a table that compares the nutritional value of egg whites and yolks, with data provided by the USDA. I've included additional analysis in the last two columns that provides the percentage of the total nutrition found in the yolk and the percentage of total nutrition found in the white.

Although I can copy and paste the chart it is difficult to read, so please read the chart here and far more information on the page.
http://www.cholesterol-and-health.com/Egg_Yolk.html

Egg whites are just proteins that's all.