Egomania is basically intolerably self-centred. In a more technical sense, it's an obsession -- an obsessive preoccupation with one's own self, usually in the form of following own impulses and have delusions of grandeur.
Megalomania is a rather loose term, and usually means have delusional fantasies of omnipotence (having unlimited or very great power, whatever 'power' might mean to that person). Interestingly, megalomania was the standard term for narcissistic personality disorder before the 1960s (so far as I recall from my psychology degree over 30 years ago).
