I can tell you some of the things that happen to me. I wake up in the morning with chest tightness and sometimes pain coughing up all of the drainage that went down there over night. Often during the day, a bunch of mucus will let go and try to go down my throat, making me feel like I am going to choke. That sets off a small panic attack for me when that happens.
I think just the mere scare of having something unexpected go down your throat can cause you to feel, as you said, like your head is spinning at the front. Just that initial scare that something is wrong even though it has happened several times for me in the past.
No fun having allergies and anxiety at the same time, I know. I would say once the crisis moment happens with it going into your chest, try to cough and see if it feels like it is coming loose. That will most likely get rid of the pain.
To calm yourself down from it, take deep slow breaths and massage the area lightly where it hurts.
Best of luck and hang in there!