Why can't I stop overthinking and why do I get moody when she takes long to reply?

Hello Kit, additional information about the context of your situation might change my answer and the following is simply my perspective on what you've written, so I may be wrong, however, it seems that you are putting a lot of focus and energy on this person and that this isn't being reciprocated in the way you would like. There are lots of possible reasons for this, these include:

1. That for one or more reasons this person is unfortunately not as invested in the relationship as you i.e. you are correct in how you feel about her not caring about you as much as she says.
2. That she is equally invested in the development of the relationship but is actively being guarded or elusive because she gains satisfaction from being chased.
3. That she is equally invested in the development of the relationship but simply has different expectations/established behavioral norms concerning the frequency of contact + response time.
4. She may have other things happening in her life that you may or may not be aware of that could be draining a lot of time and energy.

You can't help your biology and it seems clear that you want to develop the relationship but I encourage you to step back from the situation a little as overthinking and moodiness like you've described could have the effect of scaring or chasing her away if it escalates. Some people have avoidant attachment styles in their relationships with others, so it might not be that you are doing anything wrong. If your own attachment style is one that's anxious, then this will likely exacerbate the situation. It might be worth looking into attachment styles to at least gain some understanding of your own typical ways of behaving in relationships.

If you notice yourself overthinking or having negative automatic thoughts, I encourage you to interrupt this patterning process and turn your thoughts to something positive or physically begin a new activity/task. Overthinking can be extremely limited and can take up a lot of time and energy so if you are struggling with this I recommend you put some strategies in place that will work for you to begin to change this.

I hope that helps!