δικός μου is the masculine form used for masculine-gender nouns (e.g. ο σκύλος είναι δικός μου, the dog is mine), δική μου is feminine (e.g. η γάτα είναι δική μου), and δικό μου is for neuter nouns such as το λεμόνι.
I'm confused about "δικό μου". To me, it's redundant. Seems like i'm saying "mine, my own" or something.
"my own" is two words, just like δικό μου.
Δικό μου is just as little redundant as "my own" is.