Help why I was choking and now have itchy throat coughing?

I was choking on food then took a deep breathe and the door went the other way by accident and now I have a itchy throat on one side and can’t stop coughing from the itchiness, why? Am I getting sick as I’ve been driving all day with the super cold AC and it’s hot outside?

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Now I have a lot of pghlem in my throat raspy throat I don't know y
Help why I was choking and now have itchy throat coughing?
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