I have high cholesterol (genetic, I'm healthy 25yr old), should I be careful of my egg consumption? I'm vegetarian & enjoy the source of protein

I would not worry. Vegetarianism is a moral choice and I'm glad you are allowing yourself eggs -- this is important in keeping you healthy. If your hypercholesterolemia is familial (as mine is), you'll probably be on meds by the time it matters, and in the meantime I'd rather you simply stay fit than try a dietary modificaiton that will probably not matter much and make your life less easy & enjoyable.
Eggs & cholesterol. Eggs aren't the cholesterol villains we once believed because whites contain lecithin, which helps emulsify the fat. Docs generally recommend limit of couple a week. Alternative: eggbeaters, which are primarily whites with bit of yolk for color. Some brands advertise their eggs are lower in cholesterol (but they're higher in price). Doc may advise statin med to help lower cholesterol.
Not necessary. The causes of high cholesterol could be generic or diet. There's a lot of food we eat will cause elevated cholesterol, such as red meats, seafood, cheese and carbohydrate etc. You need to see a doctor to get a check up with blood work to rule out other causes. Your doctor could give you detail diet information.