According to the symptoms you describe, it seems that you are probably experiencing specific signs of what is called premenstrual syndrome (PMS). PMS is a condition that commonly occurs during the week or two before the start of menstrual bleeding and can last until menstruation starts. Symptoms are as diverse as overall discomfort, edema, weight gain, painful / swollen breasts and tenderness, abdominal distension, backache, various joints pain, constipation, weakness, dizziness, fatigue and lethargy, insomnia, depression or anxiety, irritability, headache, clumsiness, and even uncharacteristically aggressive behaviour. Women may even experience no symptoms at all. The basic cause of this state is still not known, unfortunately.
As a possible solution, yoga could help by relieving the discomfort and keeping a woman fit, strong, clear thinking and with bliss. There are poses which might appear to be particularly useful during the premenstrual period with regards to symptoms relief. These poses ease menstrual cramps, heavy bleeding, discomfort, joint pains and the low back pain associated with menses.
It is not quite clear what exact tests were done to exclude various forms of possible arthritis (and autoimmune arthritis, as well), but it might be wise to add a few laboratory analyses (if not already done), such as a complete blood count (CBC), erythrocytes sedimentation rate (ESR), urine tests, C-reactive protein (CRP), rheumatoid factor (RF), antinuclear antibodies (ANA), a few other autoantibody-tests (if needed), T4, T3, TSH, joint fluid, X-ray, etc. Meanwhile, a magnesium dosage increase as well as taking an over-the-counter analgesic (for example, ibuprofen or other NSAID after a meal, only if you don’t suffer from gastritis or stomach ulcer and if you know you are not allergic to it) might relieve the shifting joint pains.