(Question) I have had a cough for over a month. What should I do?

I've been having a lot of health concerns lately, so I'm posting this on the Cashdoc community. At first, I thought it was just a cold, but my cough hasn't stopped for over a month now, and I'm becoming increasingly anxious. If anyone has had a similar experience or has any helpful advice, I'd love to hear from you.
 
My cough first started about a month ago. When the cold symptoms really kicked in, I had a runny nose, a little phlegm, a mild fever, and body aches—all the usual symptoms. So I went to my local hospital, got a prescription, and diligently took the medication for a few days. While taking the medication, the runny nose and phlegm symptoms improved relatively quickly, and my body aches also improved quickly. The problem was that even though most of my other symptoms disappeared, my cough just wouldn't go away. I'd heard that a cough can linger at the end of a cold, so I figured it would get better in a few days, but it didn't seem to get any better. The coughing started to recur several times a day, and it was especially worse at night when I was trying to sleep. At first, I thought, "Just a little more, that's all," but at some point, the coughing became a part of my daily life.

Because my symptoms weren't improving easily, I decided to change hospitals again. I was curious if there were other causes, and I also thought the medication I'd been prescribed at the first hospital might not be working for me. At the second hospital, they suggested it might be a residual cough caused by irritated airways, and prescribed anti-inflammatory medication and an inhaler. I diligently took them as instructed, but nothing seemed to improve as expected. While the frequency of my coughing during the day seemed to have decreased slightly, it didn't completely disappear or show any noticeable improvement. A few days later, the coughing got worse again, and I started to wonder, "What's going on?" From then on, I began to feel increasingly anxious, wondering if it might be just a cold.

Then I visited a third hospital. This time, it was an ENT department. The doctor listened to my symptoms and suggested that reflux esophagitis might be the cause. I knew reflux could cause coughing, but I rarely had heartburn or epigastric pain, so it felt a bit strange. Still, they couldn't rule it out, so I was prescribed another cough medicine along with an acid suppressant. But this didn't help much either. The medicine would temporarily help, but after a few days, the cough would return and worsen. If I stopped taking it, the cough would get worse... I was getting tired of this repetitive pattern.

At some point, I started to wonder, "Am I taking the medicine for too long?" I was especially worried that continuing to take medication with uncertain effects might be putting a strain on my body. So I even tried stopping it altogether for a few days. But after I stopped, I started coughing more easily and my throat felt more scratchy. Even with the medication, it didn't completely get better, and if I didn't, it would get worse. This ambiguous state continued, and I gradually lost track of what to do. I was also becoming increasingly tired of the medication, and constantly switching hospitals was burdensome, but I couldn't give up on the treatment. My emotions were very mixed.

Wanting to find a more natural and less burdensome alternative to medication, I started eating foods known to be good for coughs. I alternate between drinking boiled pear, bellflower root tea, and honey ginger tea, and I try to drink warm water frequently. Before bed, I warm up with a shower and run a humidifier to keep the room from drying out. I open the windows slightly to ventilate, and I regularly clean the surroundings to prevent dust buildup. While these measures certainly help alleviate the sore throat and tickling sensation, they don't eliminate the underlying cough. While I may feel relief for a moment, the cough quickly returns. At night, I wake up with a cough that's even worse than during the day. The lack of sleep leads to even more fatigue the next day, and fatigue makes my cough more sensitive, creating a vicious cycle.

My current symptoms are mainly a dry cough with little phlegm. I have a persistent ticklish feeling in the back of my throat, and I react immediately if the air is dry or there's even a little dust. During the day, I can hold back my cough and talk, but if I talk for a long time, the cough often comes back up repeatedly. The night is especially problematic, as when I lie down, the cough suddenly starts violently and takes a long time before I can fall asleep again. Sometimes, when I cough for a long time, my chest feels tight or weak, and when I cough for too long, I worry more and more whether it's just a residual cough or if there's another problem.
 
Some people tell me not to worry too much because coughing itself is a common symptom, but I'm getting more and more anxious because it's been going on like this. People around me are telling me all sorts of things like it could be early-stage asthma, rhinitis or postnasal drip, reflux, fine dust or an allergic reaction, etc., so I'm getting even more confused. There are so many possibilities, so I'm even more confused, and I'm wondering what tests I should get and which hospital I should visit. I haven't had a lung X-ray or pulmonary function test yet, but do I really need to get those tests when my cough persists like this? I've been to several hospitals, but they haven't found a clear cause, which makes me even more frustrated.
 
The inconveniences in my daily life are becoming increasingly severe. Sometimes, I have to talk a lot at work, and I often feel embarrassed when I suddenly start coughing uncontrollably. I've even had to leave a meeting because I had a persistent cough, and in public, I feel self-conscious and guilty. Even if I say I have a cold, people look at me with concern when my cough persists for over a month. Furthermore, I can't get enough sleep at night, so fatigue builds up and begins to affect my daily life. My physical strength is declining, and I can feel the coughing taking a toll on me mentally.
 
Has anyone else experienced a cough that lasted this long after a cold like mine? I'm curious about what treatments helped you improve, or what tests might be helpful. I'd love to hear your advice on things like pulmonary function tests, allergy tests, and reflux tests. Also, if you have any tips for reducing your cough in your daily life, I'd be so grateful. In this time of uncertainty, even a little information can be incredibly helpful.
I've been coughing for over a month, and I'm exhausted both physically and mentally, so I'm writing this in hopes of finding some direction. Thank you so much to everyone who reads this. Feel free to leave any comments, and I'd be grateful if you could share your advice. It would be incredibly helpful.