She did once play on the zebra at 6am though, and they came around at 8am to complain about the noise. And those things do make a noise (we had one briefly and thank god it's gone now).
And she wasn't ill on that particular occasion, just awake very early and playing loudly. Fair enough, you moved the toy after that, but by then it had disturbed them early in the morning.
This may be the first time she had disturbed the neighbours or it might not. If she normally wakes at eight but you stay in bed while nine thirty, perhaps that hour and a half of her playing is a lot louder for them than for you.
Perhaps they put up with it even though they like to sleep in at the weekend, because it normally starts at eight, but felt pushed too far by it happening at six.
You yourself were annoyed that they knocked at eight, so perhaps you can see their point if her playing in her room wakes them at six or eight each weekend.
This second time is a little different. She woke up at three, crying in pain and you took her to your room, where for two hours she continued to cry and wouldn't settle.
So at five (as you said a couple of hours later) you put her back in her own room. DS prefers to settle himself and sleep alone too, so I can see where you are coming from in doing that even when she was ill. You know your child and you try what works for that child.
But instead of settling herself, you say she got up and played loudly again, at five am, which obviously the neighbours heard. It wouldn't automatically occur to them that a child playing loudly in the early hours and for the second time was a sick child.
Your DH then went into her room to try and sleep with her and settle her but she was screaming and crying and banging her head on the wall for another two hours.
The neighbours again came to complain at eight am, and again you are annoyed because they woke you.
Now if they were complaining about her crying, that would be unreasonable because young children in pain do cry. All you can do is apologise, explain, and bear in mind that taking her downstairs might be a solution in the future. Maybe cuddles on the sofa with the TV on quietly or something.
But if they were complaining about the noisy play you said she doing at five am then that's not unreasonable. They can hear her but can't see her. It would not have sounded to them like she was ill. It would have sounded like she woke up to play at five in the morning and then had a two hour tantrum because she was stopped.
I really do sympathise because I have a lot of trouble with my ears and it's bloody painful. And I hope she's better soon.
But there is a big difference between the neighbours complaining because she was ill and crying and the neighbours complaining because she was playing loudly with noisy toys at five or six am.
Maybe a warm hot water bottle or one of those microwave heatable bags against her ear will help soothe the pain in future, it sometimes works for me.