Try using gentler products, and maybe limit exfoliation (if you do it) to a few times a week versus everyday. Also, invest in a good moisturizer! Moisturization is key, so I would recommend a basic gentle moisturizer. Philosophy's hope in a jar is good, or if you want to go toward an oil, Josie Maran's Argan Oil is FABULOUS (I know, you're probably cringing thinking of putting oil on your skin therefore creating an oily mess halfway through the day). But it's the exact opposite! The oil really absorbs into skin and reveals smooth baby-like skin without the extra greasy oil. It feels heavy at first, but after you give it a few mins to sink in, it really is quite light and hydrating!
As previous post mentioned...hot water in the shower could be contributing to your dry skin in the morn. When you overly dry out your skin, your skin trys to compensate for the lost moisture and therefore creates and excess of sebum. I think if you keep skin super moisturized and avoid super hot water and rough exfoliation, your skin will achieve a harmonious balance between dry and oily!
Answered[ Edited ]
A few questions: What are you currently using for skincare (from facial cleanser to moisturizer)?
Typically what water temperature and length are the showers?
It could be drying out due to the combination of a stripping, exfoliating wash and hotter shower temperatures. The hotter the temperature, the more chance of that dry feeling afterwards (especially for those who love longer showers). Acne washes and long hot showers might also be completely stripping the face of oils causing an overproduction of oil to compensate (and unfortunately in a lot of cases, breakouts).
Use a lighter/non foaming cleanser in the shower and see if there is a less dry feeling post shower.
Post shower is probably one of the better times to start applying other skincare products to absorb. If you use toner, a little goes a long way. In this case, one without alcohol might help it from over drying the face. Apply skincare and the moisturizer gently. Since there is not enough detail, no suggestions of products at this time.
Hope this helps a bit to diagnose the problem.