As the mother of a two grown up dc who as tiniest had rank ears, with recurrent ear infections, three burst ear drums between them, and a regular traveller to France, I am appalled by the advice on this thread.
The child is ill and may deteriorate, the ear drum may burst en-route. The mother has had no sleep and there are other small children. Add I to the mix the fact that the father is probably unused to driving onto Eurotunnel and unused to driving in France where even with sat nav, significant attention will have to be paid and a passenger may need to help with lane positioning. If the drum were to burst in the tunnel, it will be distressing for the entire family, let alone the child. If as turning off/joining the auto-route or on the perifique if taking that route, it is potentially very dangerous. The child will scream, the others will cry and the drivers concentration will be shot.
Add into the mix the fact that the family probably speak no French, this could happen off the beaten track and is rather more complex than trois croissant still vous plait and there will be difficulties.
It's an insurance job. The trip needs to be delayed rather than risk an absolutely miserable time.
As for the A&E/AB arguments, it's as absurd as it's irrelevant. And never ever shoukd anything be put into a hurty ear without professional advice. As for pharmacies prescribing, is it as simple as that? There will have to be a "consultation" with a prescriber, will they be immediately available? Are they in every pharmacy? I'm also not sure whether AB's are available over the counter any more in France, certainly not for children and the opening hours of pharmacies certainly don't mirror those in the UK.
Cancel OP. Get the insurance claim in. Call Eurotunnel and Disney ASAP and take the children to Chessington/Leyland on Monday if they are better as a little sop. Rebook but bear in mind there may be a supplement if you go in high season. The insurance will only pay what you have paid.