My girlfriend saw messages between me and her friend?

There was nothing bad or flirty or me cheating in any of these messages don't worry, but hear me out..

So over a month ago I started hanging out with a girl who I'd been talking to on Facebook and one time when we were hanging out, her friends kept messaging me to say she really liked me and I should make a move.. but later on I got talking to one of her friends on Facebook asking if it was true and she said yes, and she gave me a bit of advice and things and when I asked the girl I'd been hanging out with, out properly, she accepted.

Now for the first few stages, I was really insecure about myself. I thought the whole thing was a joke at first because I couldn't understand at all what she saw in me.. But this friend of hers originally sent her a text asking what she'd say if I asked her out, and also helped me type out the whole asking her out paragraph.. and once getting together, each time I thought I'd done something wrong and my girlfriend was quiet, I'd talk to this friend asking if she was alright with her and things..
This was back in late June but I was scrolling down my messages earlier when I was with my girlfriend and she wondered what had been said, so I let her read the messages. She literally read every single message we'd sent and it kind of shows this really insecure side to me.

She did know I was insecure at first anyway and I've recently been telling her I'm so much calmer now, she seemed fine with me after the messages and I asked her for a hug and I got one. Then when her mum dropped me off at mine tonight we shared a hug and kiss as normal so she is fine about it I guess but things have started to go so well lately and now I fear these messages might stick in her head a little. I haven't spoken to this friend since then and she knows that. I also messaged my girlfriend when I got in saying I found them cringeworthy myself, she just sent laughing emojis..

Think everything will be alright? Or what to do if it won't be?
My girlfriend saw messages between me and her friend?
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