I'm afraid I don't have much time today, so I'll be quick!
On the whole, no, having a lower level of one given hormone doesn't mean having more of the other because of that. But again, I think it's important to bear in mind that there's really no such thing as a static "level" for hormones, because they are always in flux. Remember: there are at least 50 hormones in the human body we know of, not just three, and our bodies don't operate the way we often think of them, with systems separate from each other. All of our systems have interplay to some degree, as do our hormones. And again, even the common framework of "balance" or "imbalance" is an iffy one, and like so many medical frameworks, has a bunch of ableism baked into it.
I want to repeat again that your hormones -- including those involved in the reproductive system -- are always in flux, and that is very much true about estrogen and progesterone, two involved in menstruation and fertility with FSH and LH, also super big players here. And again, how mood change around events like ovulation and menstruation isn't just about those two hormones. That all said, the path to and from ovulation is actually generally pretty gradual and smooth from day to day in most bodies, not something that's suddenly chaotic. And we can have changes in our moods every single day.
Here's a good explanation of the fertility/menstrual cycles and what's happening:
https://www.scarleteen.com/article/bodi ... _about_fam The hormones that "direct" all of this are secreted by the ovaries and the pituitary gland.
I always like to remind people that pregnancy is one of the riskiest health events there is. I think that's always massively important to keep in mind when we're talking about medications and devices that prevent pregnancy. All of the current methods out there have been so, so very studied -- almost no other medications, of all kinds of medications, have been studied as much as oral contraceptives, largely due to opposition to the pill from the start -- and tested, and we know that they are generally very safe. With some hormonal methods, as, again, with all medications, there will be some people who shouldn't take it because of risks or higher risks something about them or their health, but by and large, we know what those things are. Testing for methods is so, so rigorous. Most of what people say about risks with these are based in ignorance or bias, not science and other study.
No medication is safe for everyone. Aspirin isn't safe for some people, you know?