If you are still young and working in your dad's restaurant is your first job as it sounds, it's absolutely natural to be shy. When I was 18 and got my first job working in a restaurant I was painfully shy and quit after 2 days because I didn't know how to speak to the customers and all my colleagues were older than me and very loud! Fast forward a number of years and due to having just got stuck in and trying things I didn't like my job now involves ringing up strangers all day on the phone and building a rapport with them and I have no problems. It will come with age but the important thing is that you stick at things as I wish I had stuck at that first restaurant job I had!
The christmas job application season is starting so make a real go of it and apply for everything you can that you wouldn't mind doing. The most important thing in terms of your CV is to list actual things you can already do - employers basically want to have to train you as little as possible. So don't write things like "performed a variety of restaurant tasks", write "used a till", "counted takings at the end of the day", "acted in accordance with food safety regulations", then wherever you are applying thinks "ah we won't have to train him to use a till/count takings/in food safety". Highlighting the skills you already have can give you a headstart as you seem like less of a gamble.
Good luck and don't be too self-critical, the most natural way to gain confidence is to just relax!