What can I [20M] do to improve my relationship with my girlfriend [19F]

Over the past week, my girlfriend and I have gone through a pretty bad rough patch. Lots of crying and stress. Its been tough and have decided to take a break (with clearly defined and discussed terms) for a few weeks. I know that people say don't blame yourself for problems in your relationship, but I have realized that I was actually the root cause of them. It's my first real relationship and she is my first true love. We never fight except for occasional bickering and pettiness. We have never gotten into a screaming match or anything. We really do love each other, but my clinginess has begun to push her away. I smother her with gifts and stuff too much to the point that it has become almost boring and annoying for her. We had a talk today that we really want this to work out for us and decided that we need a few weeks apart. I've been insecure in our relationship for a few months because I would always think about how she was out of my league because she is absolutely gorgeous and I'm meh. I found myself relying on her solely for happiness. Now on the clinginess thing; I have found myself obsessing over wanting to always be with her and always be talking to her and when I'm not I get stressed out. Its not good for me so what can I do to be a better boyfriend and be better for myself?

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tldr; Girlfriend and I are on a break (with clearly defined and discussed terms) for a few weeks. This is due to my clinginess and me always wanting to be with her and talk to her. I need some time to myself to realize that there are other things in the world that will make me happy as a person. What advice can you give me on doing that and fixing this relationship? Also what would help me get over the stress of not being able to see her for an extended period of time?