Symptoms of anxiety and anger are often described as some sort of energetic sensation in my chest and sometimes face or arms. Are these sensations an 'illusion' from neural activity strictly in the brain which projects sensations on their body or is there also neural activity in my chest, face or arms that they're 'actually' sensing? If so what is the nature of that activity. If not and the sensations are just an 'illusion' how is the brain creating that illusion. Also why does stretching seem to calm or make this sensation more pleasant?
Psychophysiology is totally outside of my wheelhouse, but here it goes…
Those feelings in your chest, face, arms, etc. aren't an illusion. Indeed, it's long been argued that physiological arousal (in your body) is a core component of emotional experience (e.g., James, 1884; Russell, 1980)--alongside feelings of pleasure and displeasure.
Moreover, that you have interoceptive awareness (i.e., awareness of your internal physiological sensations; Craig, 2002) is absolutely critical for your experience of emotions (e.g., Craig, 2004). For example, damage to the anterior insula (thought to underlie interoception) impairs the experience, recognition, and regulation of disgust (Calder et al., 2000; Woolley et al., 2014).
In fact, disgust experience is consistently associated with increased activation of the anterior insula (Lindquist et al., 2012). This highly consistent relationship reflects the nature of disgust: It often involves some potent internal sensation, e.g., a pain in your stomach, a bad odor up your nose, a bad taste in your mouth, and so on.
We can go through the list of emotions and potentially find some consistent and specific psychophysiological profiles (e.g., fear/anxiety involving an increased heart rate, sadness involving a lower temperature), but this has never been successful (Quigley & Barrett, 2014). There seems to be a lot of variability in physiological activity across individuals, contexts, and time.
How activity in the body and the central nervous system interact is pretty complicated (intimidatingly so). But there are lots of psychophysiology guides out there (notably by Cacioppo), and Quigley and Barrett (2014) do a good job of summarizing some things.