I also have very similar problems with my neck and upper back and shoulder, with arm weakness and hand pins and needles, as well as the symptoms you describe on your period.
For me this just started recently (for the last three periods) but I'm 48 so I'm sure some of it is perimenopause.
Over the last few months I've had a dreadful time, I've been referred for MRI scans and tested for all sorts. But nobody has found anything wrong. Since my NHS physiotherapist reassured me about my neck and arm symptoms being a minor trapped nerve I have relaxed a lot - and I notice that my symptoms have got better the more I have relaxed and decided not to worry about them.
I've had NHS physio and a private chiropractor for the neck, back, shoulder, arm issues and that is slowly getting better.
My periods are still debilitating though and I have 3-4 days where I am unable to do anything other than be in bed. On those days I am weak, shaky, lacking in appetite, dizzy, nauseous, very anxious and depressed. I'm just starting to look into whether dietary changes or other changes might help.
I recommend reading a book called 'The Period Repair Manual' (it was 99p on Kindle recently) which has various suggestions for supplements, diet and lifestyle changes to help with bad periods.
For my dizziness (which I also get more mildly when I'm not on my period) I looked at Joey Remini's 'seeking balance' website, she has some free resources if you sign up by email.
Personally I only began to improve when I conquered my health anxiety - but being tested for everything helped with this. I now realise I was in a vicious cycle. My period brought with it what I will call a physical anxiety, ie something hormonal was making me feel anxious and giving me physical symptoms of anxiety (not my mind or thoughts, though they followed the feelings). I think that this physical anxiety would pass after my period, but by then I had major health anxiety so was studying my body the whole time and every slight twitch or odd sensation was making me feel worried anxious.
Using the 'seeking balance' approach I made a decision to get on with living my life, to distract myself from studying my body and feeling anxious about it, to do various affirmations that helped me feel safe and it has helped enormously. I was making my symptoms worse by feeling anxious about them, literally my back and neck would tense and that made my dizziness worse and that made me feel anxious which got my stomach creaking and muscles twitching etc etc.
I'm not saying the same will apply to you, just sharing my story in case there is anything helpful in there for you OP.