what might help is showing your parents a recording you've done or song you've recorded.
you won't be singing live and it would be a great way for you to show them your talent.

you might feel less nervous singing in front of them next time if they know you have a gift and if you know they've heard you before.

can take it from there, doing the same for friends and building the confidence to sing in public eventually.
step by step i guess
- showing recording to parents
- singing parts of the same recording to parents
- singing/practising at home more often
- doing the same thing for friends

best of luck.