If you have a grease/oil problem, don't use oil-based make up first off! It will only make the problem worse.
Try and find organic make up if you can; the more synthetic ingredients are in the make up, the more it will irritate and imflamate your skin if it's sensitive.
:) I have incredibly sensitive skin and I have found that organic products work best for me, but give it a try and see if it works for you also.