yeah, it's a side effect of the birth control
Birth control hormones can, indeed, change a woman's pH enough to allow more yeast overgrowth. I had this problem when I was on the pill.
Treating the yeast with Diflucan or toical treatments should give you relief, but the overgrowth may recur. Then you could take Azo-Yeast to control it. Don't eat much sugar as sugar feeds yeast.
I personally have not had this kind of effect from my birth control. Perhaps you should contact your doctor about this and see if a smaller dosage/different contraceptive will help resolve this problem.
But when I think on it, I did have a friend with a similar problem as you and she was on bc as well.
It could also be a lack of clitoral stimulation. I suggest using a lubricant till the problem can be resolved.