It does for me, but usually the opposite, the oil thins much quicker for me during my cycle, sort of like my body is dumping everything it can and quickly.  Maybe because it was right before you started it was one of those accumulated 'wait' times you get right before your cycle, where you feel almost toxic as things build up right before getting ready to dump everything.  

Interestingly, I rarely get that anymore since oil pulling, the day before my cycle is the same as every other day, oil pulling has become quite the efficient mechanism for getting rid of excess estrogen and toxins that usually accumulate and instigate that whole PMS cycle.   If for nothing else it is well worth doing just for that!

Let me know if you notice any difference during the cycle, i.e., less cramping or discomfort, etc.  I sleep like a baby now and used to have trouble sleeping the first couple days of my cycle.

D.