I'm thinking it could be tracheitis or pharyngitis.
These can be caused by excess strain on the trachea or pharynx which can be from infection or started by infection but also exacerbated by lots of talking/mouth breathing etc
It's rare for them to last so long but it can happen.
Pharyngitis is common in adults who suddenly take on roles where they have to talk a lot. I got it when I went back to uni doing a degree that involved a LOT of presentations, by the January I had the same symptoms, not a particularly bad cough, GP initially thought allergies, worsening of asthma etc... Nothing worked! I then had an incident where I took a really bad coughing fit while driving on a country road, nowhere to pull over, dangerous to stop and ended up decorating the glove box! Went back to GP who DX flu! Now around the same time I had a referral to ent for my recurrent sinusitis. The ent appointment was impossible for the specialist to properly carry out cos of the bloody cough! But he noticed something about it, asked me some questions - how long I'd had it, my occupation etc and DX pharyngitis and prescribed appropriate antibiotics (GP had tried antibiotics a few times but just standard ones and they hadn't worked), some kind of anti inflammatory (I'm allergic to NSAIDs so needed an alternative) and told me not to speak for at least 2 weeks! (I appreciate that's hard to stop a toddler doing!)
And finally the damn cough went!
When I felt my chest/throat feeling similar after that I stopped talking for a week or so or at least as much as possible and I'm sure that helped avoid it happening again, plus I think the first time was in part triggered by infection - "freshers flu"
Tracheitis is more common in little ones as the short respiratory tract length makes it vulnerable. I've seen it a couple times when it's got bad enough the poor little things had to be admitted to hospital (ex nurse, this was during my training on paeds ward) it's usually as a complication of flu in vulnerable babies/toddlers. But it's rare it gets that bad.
Anyway, that's just what it sounds like to me I'm absolutely not a paeds or ent expert but it might be worth suggesting the possibility to GP or practice nurse?
Even if it leads to a DX of something none of us have thought of.
And...I see you've found a remedy. Great stuff! But I'm still posting in case that stops working or if someone else reading has a child with a similar issue, or it may even be that there's asthma and something else going on.
I found it rotten enough as an adult. As a child I'd have been terrified!
Dd has asthma but presents very typically, her first asthma attack scared the shit out of me though! Thankfully due to her presenting very obviously/typically she was quickly DX and responded well to the treatment. She's not had an attack in a few years now.
Hope he's doing much better now and you're getting a good rest.