That there isn't a polite way of saying this

[Pinkpillow22]

"Please, will you just stop talking for a while? I have my period, I am trying to concentrate and you are jabbering nonsense at me so I can't. Please SHUT UP!"

Is there?

Ask her if she's ever played the quiet game?
Throw a candy at her if she goes longer than 10 minutes without gabbing?

Mentioning your period as a reasoning behind your shitty temper is always wrong. Most women have periods of some description, yet most women find a way to cope.

'Not feeing best today, have a banging headache. Just a quiet day today' - and hope for the best...

But not feeling well isn't a good excuse, because it gives a blank cheque to talk you to death when well.

I know raving but my back hurts and my stomach hurts!

And she might have endo or pcos and have truly crippling periods. What then?

Don't make it sound like it is ok by blaming your own health.

40 hours a week yapyapyapyapyapyapyap! That is 1800 hours a year.

Ask her if she has had too much coffee. If she says no, say go and have one then.

You are in a difficult situation there OP and I really feel for you. Guess most of us have been in your situation at some point -- unless we're the talker!
First tell her how you're feeling and that you aren't able to talk to her now. Get yourself some earplugs and use them without music etc. If she tries to talk to you feign deafness . Eventually she'll understand that earplugs mean no talk.
If she does attract your attention raise your hand and say hang on until I've finished this bit and keep her waiting as long as you reasonably can. Then tell her you can only give her a minute of your time.
Good luck.

Won't chatty woman pick up some social cues from you?

..Not answering her or responding, not making eye contact, saying "Mmm" occasionally in a bored way? Picking up your whole desk and dragging it to the other side of the room?

Picking up your whole desk and dragging it to the other side of the room?

I've been known to say "I'm sorry but there are too many words happening right now"

And hope that the directness twinned with my strange turn of phrase and slightly awkward demeanour negates any rudeness. I'd rather be considered weird than rude.