A cool or warm compress is read as simple comfort laid against a hurt. Tradition sees it as care given patiently and as the wish for something to calm down and soothe.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.