Hi, and welcome to the forum.
I cant comment on the Mirena as I have never had one, but can comment on what your doctor told you ... which is, to be frank, total rubbish
From browsing this forum you will quickly see there are loads of members your age (or younger) who are peri menopausal. My initial symptoms (aged 40) were very like yours, especially the excruciating joint/back pain, dizziness, tingling, numbness and headaches. I realised it was worse before a period, but my GP just laughed as my FSH was 'normal'. If you search posts from people like Sparkle, Dogdog, Holidaylover, English Rose (and more) you will see lots of others with similarly random symptoms. I found coming on here helped me feel 'normal' again and was such a relief !
... thus followed horrible health anxiety, MRIs, numerous different consultants' visits, even a brain scan. I was petrified and lonely. Luckily, a very switched on neurologist sent me to an endocrinologist who suggested it was my estrogen levels. This was confirmed with a blood test, though to be fair, blood tests are notoriously unhelpful in most situations as our hormones fluctuate so often.
If you look at the post in new members about PMS that I added today, you will see how I have gone about sorting things. At your age, if your GP still refuses to support you and offer hrt, assuming that's a route you would consider (it is a very personal choice I know)I would suggest you perhaps ask to be put on a bio identical contraceptive pill like Qlaira which will help keep your hormones regular in a less potent way than a regular pill (it's not dissimilar from hrt, in fact).
Hope this helps. I am sure there will be other ladies who will be around to advise later x