Learn English – “X is me” or “X is theself”

"Someone like me" is the correct one.

There's a lot to say about the usage I guess, but to make a long story short:

Me is a so-called objective pronoun, opposed to subjective pronouns (I, you, she, he). It's called like this because it's placed in the object field after verbs or prepositions:

Wait for me!
She likes me.

Myself instead, is used with reflexive verbs, meaning those verbs that indicate an action that "falls" on the subject:

I wash myself.
I told myself it couldn't be true.

There are exceptions, you can find them here, but I'll paste the interesting part:

Usage note: There is no disagreement over the use of myself and other -self forms when they are used intensively "I myself cannot agree" or reflexively "He introduced himself proudly". Questions are raised, however, when the -self forms are used instead of the personal pronouns ( I, me, etc.) as subjects, objects, or complements. Myself occurs only rarely as a single subject in place of I: Myself was the one who called. The recorded instances of such use are mainly poetic or literary. It is also uncommon as a simple object in place of me: Since the letter was addressed to myself, I opened it. As part of a compound subject, object, or complement, myself and to a lesser extent the other -self forms are common in informal speech and personal writing, somewhat less common in more formal speech and writing: The manager and myself completed the arrangements.
There is ample precedent, going as far back as Chaucer and running through the whole range of British and American literature and other serious formal writing, for all these uses. Many usage guides, however, state that to use myself in any construction in which I or me could be used instead (as My daughter and myself play the flute instead of My daughter and I) is characteristic only of informal speech and that such use ought not to occur in writing.

"I can't do it" - I am not capable of doing it.

"I can't do it myself" - again I am not capable of doing it, but the myself adds emphasis on the fact that I am talking about myself, hence highlighting the possibility that someone else could do it.

"I can't do it by myself" - I couldn't do it alone.

Literally "by myself" would mean "with myself", using a sense of by that we don't really have any more. This is illogical considered on its own, but if you think of it as an answer to the question "who was you with?" then it's easy enough to see how it would be sensible to say "I was with me" and not intend it to be taken literally. These days it would be a very well-known idiom to the point where we don't even think about how those two words come to that meaning, we just think of "by oneself" meaning oneself without company.