LTM, how much sleep are you getting?
Depression and sleep deprivation make it feel like the whole world is against you in a really hateful way. Although this feels like the real truth, it's not. The illness and tiredness twist your perceptions.
Glad you've got another doctor's appointment. Well done :)
Next thing, find what practical help is available to you. Ring all the Sure Start centres and cry if you feel like it!
You need treats for yourself. Little and often is better than dramatic but few. Do what you can to get them both asleep at the same time, then take the space to have a nice bath or watch a soap, whatever makes you feel a bit more 'you'. When they're playing quietly together, ring a mate up for a chat or try on some different outfits or have a nap. Let the housework and stuff go for a while.
This next thing might feel ridiculous while you're down and knackered, but the best you can manage is good enough. The kids shriek because they want attention, right? At least half the time, they only want to feel that everything is safe and lovely. So fake it. Get down with them and give them cuddles, play interested in what they're doing, smile, tell them a story or watch kiddy TV with them. Even though you might be screaming inside, you will enjoy it (some of the time
) and it will do you all good.
Most important, I think, is to take care of you, and that includes finding help where you can. All the best.