I would add that detox reactions seem to be stronger with coconut oil than any other. It's antibacterial properties work that much faster.
I remember starting OP with coconut oil twice a day - WAY too powerful for me.
Also oil pulling can lower the swelling you have in your gums which can leave them feeling tender in some parts for awhile.
The suggestion to try different oils is a good one. Also you can just stop OP for a week and start back trying different oils or going every other day until you adjust.