I'm still figuring out the difference between the various ways to say 'I', 'me', and 'myself' in Latin. My best guess for this phrase is 'Ego sum memet', but I'm not sure which case the second word should be in, or if I should be using a different word entirely.
While one may intuitively think of using me or memet for "myself" here, the thing to keep in mind is that in your sentence "myself" is a predicative nominative - always look at the performed function in the sentence. This tells us we must use the nominative for it, that is ego again.
Therefore the phrase is ego sum ego or, for more emphasis, ego egomet sum.
In Plautus' Stichus we find an analogous (albeit specular) sentence:
Ego tu sum, tu es ego: unanimi sumus.
I am you, you are me: we are of one mind.