I would recommend a hypoallergenic brand, like La Roche Posay or Vichy.
La Roche Posay has a great line for sensitive skin, Hydreane, which you could use together with their Effaclar H too soothe the oily parts and get rid of the dryness.
From Vichy, you could try the Aqualia Thermal Serum Fortifying Moistuirizer which is designed especially for sensitive skin.