You'll likely change with age, and become confident in your ability to teach as you do some.
You'll probably find you develop 'hats' as well. Bear with me, I'm not totally insane.
See, you think of yourself as SingerPianist. Well, your first class will think of you as 'Miss SingerPianist'.
If you think of the good teachers you've had, think about what they are like, and then when you go out there as 'Miss SingerPianist' to face a class, you can adopt some of those qualities. You may find that 'Miss SingerPianist' can do things with 'teacher hat' on that you might otherwise not do.
See, I'm just me. People come and ask me to advise them on this that and the other, and sometimes I wonder why. And then I remember they aren't asking 'me as I see me', they are asking 'me as they see me, top programmer in our department in the UK'. I never wander around giving myself that label, but I find it helpful when I am asked to do something that I find scary to think that I can do things with my 'work hat' that I find hard.
What I find great with this is that when 'me with work hat' was able to travel to the US on business and spend a week being 'working Maizie', it made it quite difficult for 'me as me' to object to walking in to town on my own because it's busy and there are people and it's just all too hard. So the confidence from one 'hat' gets lent to the other hats. You find yourself actually being the person you thought you were just pretending to be.
The other thing is to remember that teachers are inherently 'different' from a pupil's point of view.
It doesn't matter if you are straight out of teacher training, aged 22, teaching 16 year olds. You think 'my goodness, I'm only six years older than them', they think 'Oooooh, teacher' (well, OK, maybe they don't; but even when you are 16 you still think of teachers as a different species).
I remember my primary school recorder teacher as being
ancient. I found out the other day that she still teaches - and that she was probably only fifteen years older than me!
Like your parents, teachers are
never young

When my mum was my age, she had my brother who was aged nearly six, and me who was about 10 months old. I can't even begin to imagine how I would cope with one child at the moment, never mind two! I can just about be trusted to look after a cat, but surely not another human being!
Talking to my mum - she felt exactly the same - what the heck was she doing, surely she couldn't be trusted to do this, how could she manage?
I think we all generally find ways to do what we have to - and I think if you really want to be a teacher, you'll find you can manage it. And I hope you bring musical inspiration to those children just like your teacher did to you