Early apples do this. They are not 'programmed' to keep. So something like Discovery is supposed to be eaten straight from the tree and the harvest only lasts a few weeks at most. Katy is the same. Something like Cox's however will last on the tree for much longer and if picked slightly under ripe will continue to ripen in store and still retain it's texture.
Your Apple must be one of the non-keeping types.

We have an old apple tree, no idea what variety. If you pick and eat it there and then its really lovely, crisp and sweet....leave it in the fruit bowl even for a few hours and as you say it turns into cotton wool....I suppose thats the pleasure of having your own tree,its not a variety that is commercial...whatever it is!

One of my trees is exactly the same, they are ready in Aug, it was absolutely loaded this year and I have placed a couple of bags in the freezer to use later but most of the crop ended up in the compost, the birds had a field day as well, my other tree had hardly any fruit this year (sod`s law) they are ready in Oct and store well for months......

May I ask why you did not purée the apples and freeze the purée for Winter use? Or did you?
We also turn any spare apples into juice which also may be frozen for winter use.
Not that there are many spare early apples. I do eat a lot of them.

We very successfully made loads of apple juice with our spare fruit this year - much better than trying to store them. The Bramleys I puréed and froze, so apple pies all winter! We used to have a "Beauty of Bath" which did exactly the same as your apples, Diamead. Terrible waste.

Nothing goes to waste with us if we can help it. Any spare apples go down the road to a farming friend for his pigs. We get some meat in exchange.