I had this problem too when I started oil pulling. It seemed like the OP was making the stains worse! I switched from sesame oil to ev coconut oil, but that didn't really change anything. Then I noticed that the stains could pretty much be scraped off with a fingernail or tool, but it took a lot of scraping. So they were not really stained very deeply, but rather something was sitting on the surfaces of the teeth. I got the idea to brush with baking soda and hydrogen peroxide, using a small child's toothbrush and really working on the "stained" areas. Miraculously my teeth appeared a lot brighter and whiter after this! So I think maybe the OP just loosens up stains or dirt and makes them more visible as they sit there on the teeth waiting to be scrubbed off.

Good luck!