How to become less insecure about myself in this relationship?

Basically a while ago I got talking to a girl on Facebook when I liked her photo and she messaged me. Conversation just flowed for ages and I really liked talking to her and we got talking everyday, and after a week she admitted that she was looking for a relationship in general and that she liked me, I admitted the sakme to her. But I didn't really think anything of it as girls usually say they like me then stop talking to me, so I never thought anything would come of it as I've been rejected and hurt by girls a lot so I wasn't too sure if she meant it or not.

We soon met up in person where afterwards she admitted she liked me all the more in person, and I couldn't quite understand why. We then met up a few other times and her friends kept messaging me whilst with her saying she really liked me but she was too nervous to say anything or make a move and later once I was home, one of her friend's text her asking what she'd say if I asked her out, screenshotted it and sent it to me. She said yes so I did ask her if she would be my girlfriend and she accepted.

We made it Facebook official just to show our friends we finally did get together, but since then I've just been really insecure about myself. She's beautiful and I find myself far from it. Like I mentioned before, I've been hurt so many times in the past it just doesn't seem real to me.
I've met her mum and dad who seem to like me quite a lot. And over these past few weeks we've all become closer and I should be really happy in this relationship and I'm not.

Whenever she's busy or stops talking when she's doing things, I just immediately start to feel like it's my fault and that I've done something wrong. Sometimes I try to put effort in and ask if she fancies hanging out and sometimes she's busy and I often feel like she's making excuses, but the more I ask the more clingy I feel I'm being towards her and might scare her away.

Now don't get me wrong, I have slightly opened up to her about my insecurities and my past, and she's stuck by me so far so that's a slight confidence boost I guess, but sometimes I just feel like I'm being lead on until somebody better comes along.

How can I just start feeling a little more confident and better in myself? Because I really don't want to push her away!