No. While similar, they have some important differences. Consider this note on usage from the Oxford Dictionaries:
The words egoism and egotism are frequently confused, as though interchangeable, but there are distinctions worth noting. Both words derive from Latin ego (‘I’), the first-person singular pronoun. Egotism, the more commonly used term , denotes an excessive sense of self-importance, too-frequent use of the word ‘I,’ and general arrogance and boastfulness. Egoism, a more subtle term , is perhaps best left to ethicists, for whom it denotes a view or theory of moral behavior in which self-interest is the root of moral conduct. An egoist, then , might devote considerable attention to introspection, but could be modest about it, whereas an egotist would have an exaggerated sense of the importance of his or her self-analysis, and would have to tell everyone