I have had this happen before. I have panic disorder and asthma, and sometimes the two combined will make me feel like my throat is tight, and will sometimes lead to even coughing and choking, or even gagging. How embarrassing it is. I think my allergies have a role in it, so for me, ice cold water and a cough drop help me to feel like I can breathe OK - an assurance you need at a time like that. For me, sometimes a real symptom (like asthma symptoms) can lead to even worse symptoms because I panic about them. Throat gets tight, but I'm OK. I then panic, and it gets even tighter, then I'm not sure I'm OK at all. It's awful.
I have read the other replies, and they are superb. I can't add to that, but I can share my personal experience. Usually once I cough a bit, my muscles relax.
I also massage my shoulders and neck, and try to relax. It's so hard to do, but the massage does help.