[Product question] I feel like my very oily skin would appreciate an oil/balm cleanser but the ones I've tried made me break out, help?

Beauty Tips For Body Care
I have really oily skin and sometimes, especially when I'm extremely oily after a long day of wearing makeup or even just sunscreen I feel like my skin would love a deep oil cleanse.The one I'm currently using (which is by Caudalie) does the job, my skin feels great after using it, clean and moisturized. The problem is the morning after I always wake up with bumps on my forehead and a few white heads here and there. The product contains sunflower, castor, sweet almond and grape oil; I have previously tried coconut oil too and that didn't work out as well.I'm not sure which product would work best on my very oily yet sensitive skin so any advice or product recommendation is very welcome! :)
Girls Blog 2015
Submitted by strangerth1ghs