Use baby wipes during your period. It sounds like some blood is getting dried around the anal area and irritating it. It happens!

You can do a double-wipe thing. With normal toilet paper I usually have to go through a couple handfuls each time anyway.

I will say it is possible to wipe from back to front and NOT include the anal area. If you wipe carefully from the back of the vuvla to the front, you will be keeping the menstrual fluids away from your anus. Then go through with a baby wipe to clean it all up a second time, and you should be good!