Could dry skin be the cause of my oily skin?

I know that statement sounds rather contradictory, but I think it might be true. After I wash my face, it's perfectly matte for a couple of minutes, but a little flaky. Then, after that few minutes is up, it starts getting shiny, not oily to the touch but just shiny. After an hour or two, my face is very oily all over, and all the flakes are gone, but my face still feels somewhat taut and my lips are incredibly dry. Could my skin actually be very dry, and my skin is making oil to compensate for that? If so, what can I do to fix this problem?Could dry skin be the cause of my oily skin?
I used to have that problem after switching to a new face wash, after a while my skin got used to it though. You could try using a face lotion with no oil and see if that helps but it may make it worse before it makes it better.