I have this problem occasionally, and was told it is tenesmus. http://www.nlm.nih.gov/medlineplus/ency/article/003131.htm
Sitz baths are supposed to help by relaxing the muscles and reducing inflammation. I didn't get much relief from them, but I think others have.
This doesn't explain the tingling in the feet, but I get that sometimes on the toilet. If I sit in a certain position it cuts the circulation off in my legs. Have you noticed that you're sitting a certain way when it happens? Leaning forward, leaning back, wide stance (ha)? When I go through these bouts I spend a fair bit of time on the toilet, with a lot of shifting around, hoping to find that one perfect position that will let my body do what it thinks it wants to do.