Myself, when used the way it is in your sentence, is not reflexive. It is giving emphasis to the subject, and it is said 'yo mismo'. It has nothing to do with the presence of the direct object pronoun.
Quite often, the Spanish reflexive verbs will not have a direct translation into English (meaning, 'myself', or the other reflexive pronouns, won't appear in the translation).
Me peino. = I comb my hair.
Me lavo los dientes. = I brush my teeth.
Me cepillo. = I brush my hair.
Me duermo. = I'm falling asleep.
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