Remarkably similar here, 10yo asthmatic son who starting throat clearing, light coughing and cold symptoms about 6 weeks back. He was actually in the middle of a trial of being off his preventer so I initially thought this was his asthma symptoms coming back because of that. After a week though the coughing became frequent, violent and horrendous, especially at night with him gasping for breath for minutes at a time, and then vomiting each time often with a nose bleed as well. We were doing the maximum of blue inhalers and it wasn't helping at all.
This was over bank holiday weekend so with no GP available we went to A&E, they gave him a course of pred and to keep at the blue inhalers, go back on his preventer at a higher dose and said it was probably his asthma.
Then we went to the GP. At this point I suspected whooping cough because I heard it was on the rise and when googling it really fitted all the symptoms. This website really helped https://whoopingcough.net/.
The GP however fobbed me off saying it was unlikely because he was fully vaccinated! And it must be his asthma. Google will tell you though that the vaccine wears off over time. They did take a PCR throat swab though to test.
In desperation, I then googled what the antibiotics needed were and found some in my parents medicine cupboard and gave them to him. This was on day 10 after his initial cold symptoms. I am not exaggerating when I say his symptoms improved 90% over the course of one day. Still some coughing at night but far less frequent and less violent.
After about 10 days after the GP visit, they called to say the test was positive for whooping cough! And to have antibiotics! Funnily enough, around this time, he had a bit of a relapse so I gave him another course which helped a lot.
We had gum swab kit sent as well which we completed about a week ago.
We are now about 6 weeks in and he is still not back to normal, still coughs now, mainly related to exercise or cold air, he is fully back at school though and having far less of his blue inhaler.
Hope you see some improvement soon, it really is horrendous for them.