"I was suddenly tired: the kind of angry-tired that’s irritated by everything that isn’t flat, and white, and has a pillow at one end."
This describes a bed. A pillow, and a white, flat, surface. This means the character is very tired and wants to sleep, and nothing BUT getting some sleep will make them happy.
‘If I thought you were that kinda guy, I wouldn’t have let you get near her, or any girl I know.’
I'm not quite sure what that means. Is there some text or conversation before this? Who is saying this?
Hope I helped, if I misunderstood, feel free to tell me. :)