I'm aware of the Sapir-Whorf theorem. It's a compelling theory; not necessarily the correct one, as science has been proven to be so devoid of throughout centuries, but compelling enough to inspire following.

Maybe we're thinking about it all wrong. Maybe there was neither self-awareness nor self-expression when language was born - not in the way we see it now, anyway. Maybe there was something less bright yet moving enough for proto-humans to communicate about. We know many animals to express themselves - not in the artistic sense but in the sense of transmitting their thoughts and feelings: dolphins, wolves and elephants are just three examples.

One of the theories of the origin of language that we were acquainted with during our Introduction to Linguistics course was Karl Marx' theory about common work (which isn't the name of it, but it describes the idea fairly well). The theory went on as follows: as humans developed in mental capacity, they found natural benefit in working in groups; to communicate within the group, humans came up with certain noises for certain things, and, in layman's terms, things just snowballed from there. Whether it includes self-awareness at this point was not stated during our introduction to it.

I'm inclined to think that self-awareness came first because it would create the need for something to be expressed, and from there it was a mutually influential progress. I'd be happy to be proven wrong or illuminated on the matter.