Knowing my self-worth

I hope one day I can achieve that I don't need another person to prove my existence's worth, or anything external to me to prove my existence. 
In a relationship (may that be an intimate one or a friendship / any kind of relationship) I always feel like I have to 'prove my worth' all the time, show why is it good for them to be in a friendship / relationship with me. That I'm worth being friends / in a relationship with.  I have this constant need to prove my worth because I don't think anyone is just going to love me for myself.  Otherwise I feel that they think I'm just a waste of space.
I know that this stems from my mum saying to me in an argument when I was 16-17, that I'm such a 'horrible person' that nobody is ever going to love me for myself.I talked to her about this since and she said she didn't mean it at all and that it's not true, but I made it my belief and it totally messed me up. I don't know how to change this belief as far as actions go.  I know (in theory) that I deserve to be loved and that I'm lovable, but when I am in any kind of a relationship / friendship / social situation (even at work), I'm always trying really hard to show that I'm worth having.
It makes me so sad that I'm like this.  I am trying to change my thinking but I don't know how to change my actions; doI just stand around doing nothing???  I would feel so useless.  I don't know how to do this.  Does anyone have any advise for me?