They are both idioms, and, generally speaking, they mean completely different things.
Out of my mind
out of one's mind
: not sane : crazy
// What a ridiculous idea! You must be out of your mind to believe that.
This is often used more figuratively than literally. People are often said to be out of their minds with grief or worry.
Out of mind
out of sight, out of mind
—used to mean that a person stops thinking about something or someone if he or she does not see that thing or person for a period of time
Saying just I'm out of mind would be unusual, but it would mean that you're not in the thoughts of anybody.
Which one to use in a song would depend on the meaning being conveyed.