You should never swallow the oil after pulling, or even just hold it on your tongue in your mouth for five minutes. The oil will be filled with bad bacteria and toxins; Streptococcus mutans are the most populous. Each tooth can harbor between 1000, in a clean mouth, and 1 billion, in a morning mouth, of these bacteria. So swallowing them after they have been suspended in the oil solution would pollute your digestive tract. Always, always spit out the oil after pulling even just for a minute or two.
If you think you may be allergic to coconut oil, try using one of these other oils, but be sure that it is "Cold Pressed." The standard commercial manufacturing of oils involves petroleum-based solvents and contain trans fats. Consider using sesame oil or sunflower oil which have been found to reduce plaque-induced gingivitis. In fact, Root of Sesame (Sesamum indicum) contains chlorosesamone which has antifungal activity, as well as polyunsaturated fatty acids that reduce free radical injury regularly occurring in the oral cavity.
You could use olive oil, but it does not contain the same antifungal qualities of sesame oil or coconut oil. I personally tried olive oil for pulling, and found it very unpleasant, and it left a lingering oily sensation in my mouth for hours after pulling and brushing my teeth.
If you can tolerate coconut in other products without an allergic reaction, I would give the coconut oil a try again, being sure to spit it out, in the trash can, at the end of your oil pulling session. Please let us know how it goes!