Which phrase does the red short message belong to?

Red and short messages are nouns, and the combined phrases of nouns and nouns can also be called noun phrases. They are coordinate relations, so they are the types of coordinate phrases.

Phrase structure types can be divided into coordinate phrases, radical phrases, verb-object phrases, predicate-complement phrases, subject-predicate phrases, compound reference phrases, orientation phrases, quantifier phrases, prepositional object phrases and so on.