Proteins are most certainly able to convey messages and by their phosphorylation state (and other modifications), are able to hold and pass along information.
Nor am I wrong about proteins. Proteins have information content - like the airways in radio transmission/reception or land lines in telephone conversations - but they are not the message nor do they constitute the successful communication of the message.
In "information theory and molecular biology" the message is DNA or RNA.
And in the Shannon model, information is the reduction of uncertainty (Shannon entropy) in the receiver (or molecular machine) in going from a before state to an after state.