I have a slightly similar quandry, OP, and face alot of the issues you do.
My suggesion: in your mind decide how long you can stick it for - the duration of your course until you qualify, for example? Then you can look again seriously at renting privately.
Private renting is insecure, and much of it at the lower end of the market is shocking. But if you hate where you live in social housing, sometimes you have take a chance.
Unfortunately, alot of councils and housing associations do not enforce standards. Where I live there are meant to be no dogs, but there are plenty of them and they do cause issues. People sell drugs and get arrested and convicted, but still they stay .... I could go on. It can get you down! Also the quality of much local authority housing is not that great. I remember my mum moving into a lovely new, decorated council flat in the 1970s. A rare event these days, you often have to spend months trying to get it to a basically liveable standard.
If you are going to leave, then you also have nothing to lose, in terms of putting pressure on the HA, or your neighbours, though if the walls are that thin, I don't think there is going to be much you can do. You COULD make yourself a real pain in the neck with the HA. Walls between neighbours have to be a certain standard - you shouldn't hear them talking. This plus the other things, they may respond. You could get your councillor/MP involved. You have nothing to lose if you decide that if it doesn't improve you are going to move anyway!
You could keep at it with the home-swapping thing. You would have to make a serious probject of it though, over the next few years, giving it a couple of hours a week. I know you've done it for years (so did I and didn't get anywhere!) but if you treat it more as a serious project, you may get somewhere.
As for private housing, its is shite. I've done it, its insecure, its horrible dealing with some letting agents, and so on. But life is for living. And if you hate where you live, and you can move, then I would personally. You don't say how old your DC is. Luckily you have the time to find somewhere that really suits, rather than just rushing from one private landlord to another. If you do it, try and spend some time finding a landlord who is good, genuine and who will treat you fairly.
Sorry for the long post! But I have been in a similar situation, and I probably even need advice myself
.. I don't quite agree with the posters who say never give up social housing, but agree its best to continue to see if you can change things in other ways first, before giving it up!