Oil pulling vs. brushing with coconut oil?

Hi

I'm sorry if this is an oft-repeated question but I was wondering if brushing teeth with coconut oil would give the same results as oil pulling. I have tried oil pulling for several weeks but I swallow some of the oil each time. Because of this, I get a stomach ache everyday and my dark circles have gotten much worse. 

I recently found a recipe for a DIY toothpaste online. The main ingredient is CO and the others are baking soda and essential oils. I would like to know if this would be as effective as oil pulling for oral health and gut health.