It is not used in a sentence. Ughness is a state of being. When you dislike something; disagree with something; feel lousy --> you/that entity is said to be ugh.
ie// It was raining and my hair is frizzy, ughness.
It is a term used when you are angry, annoyed, disappointed or disgusted. "Ugh" is the key part in this word. You can add "ness" to the end of many short descriptive words, it gives them a stronger meaning.
Guy: "Hey, do you wanna hang out or somethin'."
Girl: "Yeah, sure...wait ughness, I have to babysit my sister. Sorry."