Is it okay for mom to give away something given to me as a gift?

Of course not. From a legal standpoint, this would constitute theft of property in that your mother has transferred ownership of real property (your shirt) not only without your permission but over your objections. That said, it really does not sound as if the shirt is your major issue, it sounds as if you feel that your mothers treatment of you is not what you feel you deserve. I can't tell you how to handle that other than to say that you will need to speak openly and honestly with your mother regarding your feelings if you ever want anything to change.