This happens to me also - I've been doing OP for years but doing it twice a day did make my teeth sensitive. I cut down to once a day and it helped, and switching to flax seed oil from coconut helped more. I do flax seed most often but mix in coconut maybe a third of the time.
Though I'll admit I don't do it every day. Even though that's recommended, every other day seems to work fine. Even once a week is far far better than none at all.