Sounds like Post-Nasal drip, from the nose.
Then the person "coughs" because the nasal secretions/mucus goes down the throat, and then it accumulates, and causes the "gag reflex" to trigger. Hence, coughing.
And when laying down, the mucus drips from the post-nasal drip... accumulates in the throat. Hence triggering the gag-reflex/coughing.
Hence that icky feeling there. Because the mucus is accumulating in the throat.
And sometimes, the mucus from the throat will go into the chest. So the cough sounds "deeper."
Coughing, originates from:
1) the sinuses (post nasal drip) or,
2) the chest
3) or both
There are nasal drops. ie: "Little Noses" nasal decongestant for kids. Gotten from any drugstore. It helps a lot.
Claritin etc., is an antihistamine. THUS, it may not target the "nose" per say. Thus, it may not work, for nose issues.
Thus, use a NOSE decongestant. Because THAT, will target the nose and its stuffiness and mucus.
Keep in mind, that some people just have sensitive noses to dust or anything in the air. And things in the air, cannot be completely gotten rid of. Also keep in mind... that "dusting" AND vacuuming... kicks up a LOT OF DUST, while it is going on. You cannot "see" all this dust being kicked up... but it saturates the air, while it is being done. My Mom's Allergist, told her this. He told her, DO NOT BE in the vicinity, while vacuuming is going on. Not for an hour afterwards etc. Because, the "air quality" of the air after dusting/vacuuming, will be full of dust. Until it settles down. Atmospherically.
I have sensitivity to air dust, not "allergic" per say, but since I was a child I was like that. Now as an adult, I take Claritin or saline nose drops or even my prescription "Nasonex" if I need to. BUT only if I need to. Because most of the time, it is not severe enough for me, to have to use it every darn day.
THEN, what is the air quality in your area or weather? Is it smoggy? Dry? That can affect some people.
Get an air filter or purifier, for your home.
Inhalers, like Albuterol, are bronchodilators. It targets the lungs. NOT the nose. It also does NOT target, "mucus." What it does is: it opens up the lung's airways... because it is inflamed and thus constricted. Hence per Asthma, it makes a person unable to breathe. I know this because, I have had Asthma since I was a child.
Is your son, able to, or knows how to... SPIT out his mucus???? If not, teach him how. Then that will also help, to expel the mucus that is accumulating in this throat.
What has the Doctor said? Did you take him to the Doctor?
Has he had antibiotics?
Maybe he was sick but you didn't know it?
When you pulled up the carpet/tile and put down laminate flooring... there are fumes that gas off too. From the materials and glue etc. And yep, dust. AND keep in mind, that even if you "dust" the house... microscopic "dust" can even saturate the..... sofa fabrics, any fabrics, too. Including, clothing. And you can't see it. Did you vacuum... the sofas? Chairs? Drapery? That can be a repository of "dust" too.
AND depending on "how" you dust the home.... the dust can simply be flown off to some other surface. And the dust is not actually, gone. Just relocated.
Use microfiber dust cloths, that the dust will adhere to. Not just a feather duster, because those just fling the dust off to other places, and even to the floor. It does not go away, just because you "dusted."
Again, try getting an air purifier or filter, for your home and for his bedroom. Keeping it in a room where your son hangs out most of the time.
Also: does your son have Eczema? Eczema is an "inflammation." And it can sometimes, cause coughing.
Or if anything, have him allergy tested or see an ENT.