If you believe you are the most talented, charming, intelligent person on Earth then you are egotistic (or a politician): in other words you have too inflated an opinion of yourself.
Egotistic is derived from the Latin word ego for "I." Don't confuse egotistic with egoistic, which is essentially a moral philosophy that believes all human actions, even the most seemingly selfless, are guided at heart by self-interest. It's possible to be egoistic without being egotistic, and vice versa.