actually, the majority of the protein is in egg whites...
and they idea of eggs causing bad cholestorol is a bit of a myth. yes, the yolks contain fat, but it's mostly polyunsaturated, which can actually lower you cholesterol levels. also, many of the nutrients are in the yolk.
you need to monitor your fat intake in general whether it's from eggs are another food source. eggs on their own are perfectly healthy, but it depends on the rest of your diet to determine how much of them you should be eating.
i currently go through a dozen a day and my HDLD was 62 and my LDLD was 51... my doctor said he's never seen someone with such good levels as it's rare for your HDLD to eclipse your LDLD. So eat eggs