If the coconut oil is what caused the rash, it's doubtful it would be an infection. Coconut oil is anti-bacterial itself.
It sounds more like either an allergy to coconut oil or an auto-immune reaction. One day i brought goji berries over to a neighbor to try. Goji berries - the most harmless substance on earth! She developed a terrible rash over her arms and face, and had her throat swell up.
I had plenty from the same batch and nothing. But she had an autoimmune disease that immediately reacted to them.