Hello there,
I am 19, and have Asperger's. I hope I can help ease your anxiety a little
. First off, sudden changes in our lives (such as a marriage breakdown, for example, if I may use yours as an example), are not taken well. It's because we've gotten used to life as it is, and have our little routines that we must follow. His hand washing sounds as though he is worried about germs and falling ill, and by thoroughly washing his hands he can soothe and assure himself that his hands are properly clean. I know, because I went through this with hand sanitiser, and have only just recently learned to cope without it, and just use ordinary soap instead. It also sounds like a coping mechanism, i.e. if I wash my hands for this long, then I know things will be fine
In regards to the depression, I wonder if there are a multitude of issues (unspoken) ones, that have piled up in his mind, making him feel as though he'll never "get on top" (i.e. sort those issues out, whatever they may be), and thus he sees no way out. I know, I have been there, it is a horrible place.
All the symptoms you talk about point towards Asperger's, however, I'm not going to be so presumptuous as to say your son has Asperger's, I'm not a psychiatrist, and it isn't my place to say. Also, Asperger's presents itself differently in each person with it.
Why not ask the GP and psychiatrist to make a house call, due to the nature of the situation? I think the reason why he doesn't want to leave the home is because it is "safe", i.e. predictable, he knows what will happen at certain times of the day with people and their routines, etc.
Living with Asperger's (and around it) is a daily struggle, but there is light at the end of the tunnel, but you will get there
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I hope I haven't inadvertently stepped on your toes OP. If I have, I apologise.