I think this is a good thing that your T is a specialist and isn't upset at all by finding another aspect of yourself hidden away...and that part of you feeling comfortable with talking with the T, too!
I'm sorry you are distressed and scared. Please realize that singletons also have "parts" of themselves...the difference being we have the continuity of time... where you "lose" time when a part of you does something (and you don't.) Our inner children come out...but we know we are just acting "silly" and allowing it. The lack of control might be part of what is scaring you.
Don't be afraid of any other aspect of yourself...it's an indication that you suffered something you couldn't handle by yourself at the time, and that you have used a marvelous coping response to get through it. Also, don't be afraid of the memories... they can't hurt you now, and often our brains don't store the memories totally correctly.
I think it was a good idea, also, to write. Pick up a nice journal/diary (since it sounds like your other might be younger?) and encourage writing in it...you too! Be sure that nothing that is written will 'get you into trouble" nor your other part... that way you will learn more and more easily.
I think having a T who understands you is one of the best "things" you could find!!! Be sure to share your upset..perhaps the end of each session could be spent on her assuring you all is well?
Stick around, there are many ways to cope and compensate for normal symptoms of DID (such as losing time.) Once you have an understanding...things will settle for you some, imo. Take care of yourself.