Don't really know what to say, except for offering some emotional support. I think the best thing to do at this point is to take things apart one thing at a time and see what you NEED to deal with and what can be put off until you're better able to cope.
Paed appt - unless the paed is going to bring anything new and instantly relieving into the mix, waiting until January isn't a huge deal (at least for us). If he can't be seen until January, at least that's one less thing for you to deal with now. Put it on the shelf and it can be dealt with later.
DLA renewal - yes, that's obviously more of a priority. But make sure if you can get help filling it out, that you get help. No point stressing yourself out if going it on your own puts you over the edge. And the DM can piss off with their "simply fill it in to get benefits."
The words "simply" and "DLA" just do NOT belong in the same sentence... EVER. Give yourself a reward to look forward to once you've completed it - even if it's just chocolate, wine or a hot bubble bath to enjoy it all in. 
GP appointment - not until next week. Medium priority. Jot down anything you want to discuss as you think about it, and put it aside until the appointment. If you're anything like me, you tend to obsess about upcoming stuff and it's exhausting. I'm finding that writing it down and putting it aside allows me to mentally put it away until later, thus reducing my stress a bit.
As far as our DS's behaviour driving you spare, not sure what advice I can offer. I do try with DS2 to remind myself that he is actually NOT doing it to make me crazy (that's just an entertaining side effect I suppose
), and that it does NOT make me a bad mum to allow him some free time each day to do something he likes and obsesses over (such as laptop time or a much watched DVD) just to give me a few minutes to breathe and have a coffee or simply relax for a bit (or god help me, actually clean!
). That free time for him means free time for me... and that is something that maintains that sanity for just a bit longer IYSWIM.
OOooops!!!
For someone who didn't know what to say, I rather bungled on for a while there. Sorry! Hope you feel a bit better soon!