Is oily skin more prone to getting scalp foliculitis?

Yes: Scalp folliculitis can be caused by fungi, viruses and even a low grade staph infection if you are a colonizer of staph, meaning staph resides in your nostrils and belly button. A culture of both will diagnose this and it is easy to eradicate. Pathogens grow best in oily skin. I would use an anti-fungal shampoo like Nizoral for two weeks, first. But definitely get the culture. Emuaid is also good