There are several things going on at once when you oil pull, especially with cold-pressed organic coconut oil.
1) You're initiating the production of enzymes in the mouth
2) You are absorbing some of the enzyme-combined oils
3) Caprylic Acid, Capric Acid, and Lauric Acid get circulated into the veins and lymphic system about your head and neck
#1 - this is pretty normal, enzymatic processes are how the body does it's work. Making sure you're replete in magnesium (magnesium chloride / magnesium oil on the skin is the cheapest, best absorbed and cheapest) can help maximize that process.
#2 Generally a good thing, it helps strengthen the tissues around the mouth (fx, skin, nerves, muscles, gums)
#3 These three parts of coconut oil are likely what's giving you your headache. They're strong against what's often called candida infections, which is a cell-wall deficient digestive bacteria. Bacteria without cell walls (a pleomorphic adaptation of bacteria to ensure their survival) act like a fungus, and colonize where they can. They grow pipes called hyphae, which have protiens that fool the immune system from attacking and detatching them by having the same protein structure as human tissues.
Caprylic Acid, Capric Acid, and Lauric Acid are all pretty unfriendly to bacteria that have lost their cell walls and have gone into hyphal (colony) form. The acids are part of the coconut's mode of preventing bacteria from breaking it down (digesting it).
By oil pulling with coconut oil, you're getting some of those antimicrobial agents into the bloodstream and lymph, and I suspect you're killing off some infections that have been otherwise happily living all quiet and sneaky in those areas. Yes, oil-pulling with coconut oil could potetially cause sores in the mouth, because of the dieoff effect and the body needing to push out the stuff that's croaked. (candida and stuff gets backed up in the lymph system if you've got a larger
parasite problem, and then you end up with swelling/aching sores where the material is trapped. )
I'd consider a
parasite cleanse (one focused against fungal infection in the gut) in this case.
Using different types of oils (like cold-pressed olive oil) is also good, as you'll get a better range of nutrients from different oils.