My another account is not correct; it is correct to say my other account.
Googling for my another, I found many instances of the phrase, but none of those are correct: sometimes who wrote it meant another of my […]; sometimes who wrote it simply meant my other.
* That is my another problem. (That is another of my problems.)
I have been suspend from my another accounted!? (My other account has been suspended?)
* My another acc. is locked, I cannot login! (My other account is blocked. I cannot log in!)
* Could you please check my another essay. (Could you please check my other essay?)
* This is my another friend's profile. (This is another profile of my friend.)
Looking for my another on the Corpus of Contemporary American, and Corpus of Historical American, I found two instance of the phrase; in both the cases my another replaces my mother, and it is a transcription error, as my another is not used to mean my mother.
CARREY: Yes, for me, my mother was in pain all the time. I wanted to fix her. She was depressed, so I wanted to make her laugh. But I remember when I was eight years old actually having the thought that I want to make my mother believe she gave birth to a miracle. That was the conscience thought I had, is that I want my another to feel like her life was worth something, that she did something special. And I was going to be that something special.
KING: A conscious thought at Eight?
CARREY: Conscious thought at eight years old.
KING: Did you help her?
CARREY: I did in certain ways and I couldn't in certain ways.
—Interview with Fran Drescher; Jim Carrey Discusses Movies, Comedy and Relationships.
"I wasn't trying to hurt my father." He looked down. "I love my father."
"Then tell him so," said our mother.
Caleb looked at our father. "I'm telling you so," he said.
"Don't you love your mother, too?" she asked, smiling.
"Yes. I love my another."
"And your brother?"
He looked at me and his face changed. He smiled again, and he pulled me to him. "Yes. Oh, yes. I love my brother."
—Bloodline, Ernest J. Gaines.