"I have no pillow."
Translation:Jag har ingen kudde.
I assume you mean Ingen instead of inte? (Ingen, inget and inga) are , for lack of a better word "Noun negatives" or "things you can count" that match up with the respective "ett" or "en" word. (inte) is for "not". in some cases ive seen them interchangeable like... "jag har inte barn" or "jag har inget barn" .
someone correct me if im wrong, or if there is a more correct way to think about this.
"Nån" is the shortened, informal form of "någon", which in this context means "any". Literally it means "I do not have any pillow". "Inte" is a verb negator, the word for saying you do not possess anything at all of something is "ingen" for en-words, "inget" for ett-words, and "inga" for plural words.