Do oils in hair products cause blackheads?

I have blackheads on the side of my face, I think my hair products might be causing them. I wash my face twice day and night with Neutrogena ance bar then use neutrogena oil free moisturizer. On my hair I use Garnier Fructis leave-in conditioning cream & anti frizz serum - sleek & shine. Both these leave in hair products contain natural oils. I use them when I shower at night and sleep in them. Could the oil in the hair products rub off on my pillow and absorb in my skin causing breakouts? I try to keep my pillow clean. Any advice? Please & thank you!