Facial care recommendations

I recently had a few huge breakouts from the Johnson&Johnson clean and clear facial wash. I have dry and oily skin (kinda odd). As in, take my nose, for example. It's really odd. It's dry with bumps so big they are visible if you are standing near me. When I use lotion (only really good lotion, and occasionally) it smooths out, but the bumps are still visible. For example, almost every time I use coconut oil, but it doesn't last long. I have had weird puffy dots on some parts on my face for years. I have acne. My face is oily in a lot of places.
I'm looking for a good facial mousturizer and face wash (I like the "tingly" cream ones with menthol the most) that will help me with That. I'm trying not to spend more than around $10 on each (I'm cheap heh). Anything that would be available at target; I live right next to it and it is the most convenient.
So, any recommendations? Thanks ^^