But I can't stop looking back over me and my exes old messages, am I not truly over my ex or is this normal?
Maybe you want to analyze your behavior, or the behavior of your ex. Sometimes we want to find out if we were being a dirt-bag and if maybe we have outgrown that yet, or we want to realize different patterns our partners make. Perhaps you miss things about last year that may or may not be related to your ex, and that's a way to sort of return to those moments. There's nothing wrong about wanting to reminisce a bit over feelings or nostalgia, and things you did then. It could be that you just want to process things. Since your relationship only ended last Summer, and you already have a new partner, you might not have had a lot of time to move on in-between people.
If you're the sentimental type, you might be hung up on a certain ex. Sometimes it can be difficult to move on from situations that felt like they didn't receive proper closure, or where you felt you were wronged in some way. It might not necessarily mean that you aren't over the person, but you might feel like you gave a lot of yourself to that relationship, and still hurt from it. But you could feel like you seemed like a good match, and keep agonizing over why things didn't work.
You of course might not be over your ex. Some people might stay in your mind for years. But usually after a certain amount of time you realize that this person wasn't right for you for whatever reason, and that is why you broke up in the first place. People have gotten back together before - maybe they didn't give things enough time the first time around, or maybe one or both partners made some changes.
Right now you're with someone new. Is this going well? Are you happier? Is this person good for you? Relationships take time and effort to make them work out. And make sure you're not with someone just for the sake of not being alone. Being alone isn't fun, but being with a poor match isn't either. Look over those old messages if you feel you should, but if you think it is holding you back and want to put the past behind you, delete them and move on. If you feel you need closure, maybe you can still get that, but realize it might be difficult now that you are with someone new who might not appreciate you trying to reach out to an ex. I think it's best to focus on the present, and move on.