Nicodemus, desogestrel actually gave me migraines
I'd never had them before in my life and after a year on desogestrel I started to get them - without aura. I didn't make the connection with the deso though, and neither did my useless GP (really not clued up on women's issues and hormones, a bit dismissive) - he just gave me sumatriptan. I found that sumatriptan worked great for the migraines but gave me heart palpitations (I seem to have a heart which is a bit sensitive to drugs!) so I didn't take it and just struggled along with a Cephaly device (a TENS machine you put on your forehead, for migraines). I went on like that for about 8 years...
Then I stopped desogestrel and started HRT - and I haven't had a single migraine since. At that point, I didn't know if the migraines had stopped because I was replacing estrogen (and desogestrel had suppressed my estrogen - so they were caused by low estrogen) or whether there was something else in desogestrel which had been causing them.
However, I got an answer to that because I had to restart the desogestrel whilst also being on HRT (because I got an endo flare up). So then I was on desogestrel AND HRT. And with estrogen from the HRT, I still didn't get any migraines....
So I concluded that
the way that the desogestrel had caused my migraines was via causing low estrogen. (Sorry that was a v long explanation but I feel like this last year I have done little else other than try to figure out my health

) I doubled my utrogestan to 200mg daily and was then able to stop the desogestrel again, so I'm not taking it now.
I also had VA, beginning with scratchy prickly discomfort in my vulva and a glue-like discharge (interspersed with a watery one). Since starting local estrogen all that cleared up in a couple of weeks. I had constipation, flatulence, brain fog, couldn't concentrate, night sweats, weird weight gain (like could eat an apple a day and put on weight kind of weight gain!) and more. Every symptom that exists.
Like you, my FSH is still low (4) (I assume that's the same as what you mean by your GP said you are still fertile after blood tests). It was only when I read Lara Briden's book 'Hormone Repair Manual' that I realised this meant I should still be cycling and producing my own estrogen.
I also had zero sex drive or libido on desogestrel. I tried so hard but it just wasn't there. I just gave up that part of my life because I thought I 'had' to take desogestrel to control the endo. I've got that back now.
So basically, I was on desogestrel for 9 years and it led to really low estrogen symptoms which mimicked menopausal symptoms. All those symptoms resolved immediately I started taking HRT - whether I was on deso or not - which supports the idea they were caused by low estrogen rather than some other aspect of deso. My FSH was only 4 so I should still be cycling if it weren't for the desogestrel and we can conclude that the deso was the cause of the low estrogen.
To support that, my estrogen levels about 7 weeks after coming off deso were 233pmol with a 50 patch (ovaries still waking up), then at about 12wks off they were 453pmol - on a 37.5 patch. Showing that the ovaries were now making more estrogen again, since desogestrel had released them... Now I've come off the patch I don't seem to have any of my low estrogen symptoms back yet.
So - I don't actually think I am properly peri yet. I mean, I might benefit from cyclic progesterone (as Lara Briden recommends) but I don't think I need estrogen yet. (Which is good because I appear to have major issues with taking estrogen which isn't my own - and I don't know what I'm going to do there.)
I think desogestrel is a RISKY thing to be taking if you are a peri woman who wants to be maxing out her own estrogen. And I think GPs should be much more aware that it can cause this low estrogen state which mimics menopause. I guess you could just override it by taking more HRT estrogen, but there are probably many women out there on HRT who don't really need to be yet - it's just that the desogestrel is suppressing their own estrogen.
As for what you should do, if I were you, I'd switch the desogestrel for utrogestan....