There is reason for the invention of Emojis: Text is a poor vehicle for the identification of emotion, because the presence of 'emotive' words is not necessarily a sign of the presence of emotions. But there is also a reason for the proliferation of them: the expressive systems that accompany talk (intonation, rhythm, the facial expression group, etc) are far richer and more subtle than the entire set of available emojis, even today. Even so, many people can 'fake' emotions. WE are all, to some extent actors.
However, if you have a corpus of texts and evidence of the emotional reaction of competent communicators to particular textual characteristics, you can treat textual characteristics as proxies for emotional content.
Simlilarly, modern digital speech analysis can detect the effects on speech of various forms of muscular tension on speech production, some of which are too subtle for some hearers to recognise. Also, there are effects of individual 'style' in speech that allow hearers familiar with an individual to recognise emotional states that strangers may miss.
As to critical analysis, it is essentially about differences in capacity to shape 'reality'. That shows up in asymmetry in the kinds and frequency of emotional expression, the consequent power to shape the emotional context, and the way in which that maps on to social identity and roles, power structures etc.
It is more important to be sure any 'system' of analysis you use does the things I have mentioned above than faithfully sticking exactly to the system.
From left field also. CDA fits a certain set of assumptions, logic and purpose, with its 'textualism' attracting some criticism for various reasons, including the (non) correlationism of language/text/discourse with 'experience' (broadly defined) and its historical structuration (let's leave aside various comparative studies of numerous ontology-epistemology-axiology tensions, and implications for methodology, including methods/techniques like CDA).
Nonetheless, to partially assist your question, some valuable background reading I have found very useful on the question of representation and non representation (and affectivities/aesthetics of the self/others), includes, amongst numerous others - far more detail than I can summarize here.
Lakoff, G. & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought.
Thrift, N. (2008). Non-representational theory: Space/politics/affect
and, more practically
Pink, S. (2009). Doing sensory ethnography.
In different ways, these 3, at best partially, struggle with the 'ultimate' question for 'social' researchers (anthropocentrically limited) of ACCESS to (human/social) experience. CDA is a 'quick fix' (if that), and its limitations need to be acknowledged (openly), as indicated by Robert Young.
I didn't see your note by the way. I think you can use " the etic/emic" approach" to account for the interpretation of emotion embedded in certain textual materials or genres which evoke such emotion in the reader. This is an approach used for cultural analysis and it can be used also in discourse analysis. It is anthropology-based approach. It is founded by a reputable cultural linguist K. Pike. I can send some helpful material about the application of this approach to various genres.
yes, you may apply the "etic-emic-etic approach of K. Pike to account for emotive-ness . This approach can potentially allow you to account for the hidden level of meaning which may not be accessible to the target readers. I assume you are doing research relevant to translation or culture. I hope you find my comment helpful and of interest to you. good luck.
I would recommend Sarah Ahmed"s The Cultural Politics of Emotions, which casts light on the relationship among language, social structures and bodies. Combining queer, feminist, and Marxist theories Ahmed emphasizes the pertinence of considering emotions in tandem with the circulation of bodies and the social meanings attributed to such bodies in connection with gender, race, class, sexuality, and ethnicity. Emotions, hence, circulate through the materialization of bodies in repeated social discursive acts.