Wish I knew how to help you here, CuriousCat. I was a quiet child in school, but people did not bother me. I like to give personal attention to people and help them. You get to do that every few minutes with someone new on your job, and they need your help. You would be my hero at those self-serve checkouts. I always have trouble.
On public speaking...I've had to do a lot of that over the years at jobs or organizations (or in front of our State Congressmen in session, on a webcast, for goodness sake!). It is only hard if you make it hard. No one in the audience could do any better than you, as long as you know your topic and your audience, you'll prepare and be fine. It gets easier as it goes.
Let me ask you this, when you are in the audience, do you criticize the speaker? NO! And people will not criticize you. Almost everyone is afraid of public speaking, but it isn't nearly as hard as it seems.

You will do fine. Just look at a few people you have picked out and move your eyes back and forth between them. It will appear like you are looking at everyone, but not so scary.
Here is something my mom told me many years ago and it has helped me:
KarenSue, you are not better than anyone else, but you are just as good!
Best of luck to you dear.