There is certainly some overlap, but are the two words technically interchangeable?
Someone who is egotistical is egocentric; someone who is egocentric may or may not be egotistical.
Egocentric people think primarily of themselves; they are the center of their own worlds, and little else has relevance.
Egotistical people also think primarily of themselves, but have the additional tendency to think only good things about themselves.
Someone could be both egocentric and self-loathing, self-obsessed and self-despising; many people with clinical depression, for instance, can be described in just that way.
Being egotistical and self-loathing in the same moment, on the other hand, is harder to imagine, though someone could certainly vacillate between the two states.
"Egotistical" means to think very highly of one's self, usually understood to mean unrealistically highly. "Egocentric" means to think only of one's own problems or concerns, or someone who doesn't care about other people.
They're certainly related, as someone who thinks he's the most important person in the world would presumably think that his well-being is the most important thing in the world. And the kind of personality that would be one is likely to be the other.
But they're not really synonomous. You could have a very realistic appraisal of your own strengths and weaknesses, and still be worried only about your self. Or on the flip side, you could think you're the most amazing person who has ever lived, and then conclude that this means you have a responsibility to help all those less able than yourself and be very self-sacrificing.