If everyone with symptoms now calls the line, you will block the line for the most who really need it. The people on the other end can only help with one person at once and the threshold for calling that line has risen.
I’m not near your child, but if you think he has complications or you are seriously worried, you should seek further help. The guidance says you should use the 111 coronavirus service if:
• you feel you cannot cope with your symptoms at home
• your condition gets worse
• your symptoms do not get better after 7 days
General guidance for flu is clear though: it is self management for 7 days. Unless your child needs medical intervention, you will just be told to self isolate them for 7 days, and then possibly yourself too, if you become symptomatic too or the guidance changes further. Even the best doctors in the world will just give you understanding and painkillers of choice.
The overwhelming majority of children who get this will be a bit ill, but will be fine. It’s the elderly who are at risk here.
I think you are worrying too much about authorised absence. If you’re following the published guidelines, you should be confident you are doing the right thing. The online guidance from the NHS is of far greater authority than the admin person at your child’s school. There will be millions of kids off sick soon following the guidelines. I wouldn’t worry about that.