How can I stop somatic anxiety symptoms like chest tightness?

I used to get this all the time. Box breathing (inhale 4s, hold 4s, exhale 4s, hold 4s) really helped me get through the worst of it.

In addition to breathwork, Progressive Muscle Relaxation (PMR) is highly effective for somatic anxiety. Since your body is subconsciously tensing up (hence the chest tightness), PMR teaches your brain the difference between a tense and relaxed state by intentionally tensing muscle groups for 5 seconds, then releasing. Start from your toes and work up to your jaw.

Somatic symptoms of anxiety occur because your amygdala perceives a threat and activates the sympathetic nervous system (fight-or-flight), flooding your body with adrenaline and cortisol. To counteract this, you need to activate the parasympathetic nervous system (rest-and-digest). The most effective, immediate way is through your breath. Try the physiological sigh: two quick inhales through the nose, followed by a long, slow exhale through the mouth. Repeat this 3-5 times. The extended exhale physically slows your heart rate via the vagus nerve.