Linguistic Analysis: "...tends to focus on formal features of a language at phonolgical, lexical, syntatcis, and pragmatic levels." (Xiaoye You, 2008)
Rehetorical Analysis: "An efort to understand how people whinin specific social situations atemtp to influence others through language." (Selzer 2004 quoted in You 2008)
Discourse Analysis: "the analysis of spoken and written language as it is used to enact social and cultural perspectives and identities." (James Paul Gee, An Introduction to Discourse Analysis)
It seems like you could and maybe should do them all at the same time.