ALWAYS lingering cough after cold

Hi, I'm 19M, 5'11 140lbs, and a pretty healthy person

I just got sick for the first time in almost 6 months last week - it only a couple days, and I've been over it for 4-5 days now. And I'm remembering the constant lingering cough that I always get after I'm sick

As in, every single time that I've gotten sick in the past 5 years, I've had a lingering cough for about 7-10 days afterwards. One time it went on seriously for two weeks, and then slowed down, but kept going as a very mild cough for about a month straight (mild as in, maybe a medium cough every 5 minutes)

it's always a super dry cough, never phlegmy or anything like that, just hacking out a cough every 30 seconds or so. And they aren't just little "ahem" coughs, they're full force, hard coughs that I have to stop and focus on.

It's very annoying. I have a terrible gag reflex, so on the (very common) occasions where it'll randomly make me cough 5 times in a row, I'll start gagging from just how nonstop I'm always coughing. It also gets to a point, such as right now, where it's been going on for 5 days straight and the back of my throat starts to get pretty sore as a side effect of it.

Also, medicine and suppressants don't seem to do anything for it. Cough medicine has a slight effect at suppressing, but not for long. Cough drops do absolutely nothing. Various liquids (gargling saltwater, cough tea with honey, etc.) don't do anything.

Why is this? Is it anything "worrisome" of my body, a sign of any sort of deficiencies? Can I do anything about it? I wouldn't be worried at all if this was just a one time thing, but it's been 5 straight years