Oily skin with moisturizer but dry without

Ohai!
I'm a bit confused, I wash my face (almost) every day and when I use moisturizer for normal/sensitive skin my face gets oily.
When I don't user a moisturizer (so just washing) my face will instead feel dry and a bit rough even, especially in the t-zone and it even gets itchy.

I am confused. Do I have dry skin? Oily? Halp plz.