Hi Gwenny -
Yeh....deadlines. Don't get me started :-) Most of the 'helpful' stuff out there assumes that you're in reasonably good health. And as we know, that ain't so, at least for a while, for most addicts in early recovery.
Nevertheless, you have this deadline. Just in terms of that immediate pressure, are you able to simply contact the publisher or whoever gave you the contract, and do some straight-up re-negotation around the deadline thing, both for the immediate present and near-future. In other words, re-calibrate the whole-book deadline. Let's face it, they can stick to this mythical deadline all they like, but if you can point out the bald facts to them that while you're recovering from an (unspecified) 'illness', the drafts and then finished product from you are not going to be to the required standard.
Sorry to sound blunt about it, but I believe now, after many years, whilst both drinking and sober, of trying to force my self into external pressures like this, that my own self-care MUST take first priority above all else. If it doesn't, then I end up anyway in the terrible feedback loop of shame, frustration, massive worry and stress (about what these 'other people' will think of me, whether they'll ditch me as a viable prospect - professionally or personally, and blah and blah and blah :-)). As us alkies all know, that added shite we put on ourselves can far too easily send us straight back into the bottle. Just like you described, in terms of the illusory but automatic temptation to drink to soften the pressure and stress...the F*^^k it factor.
Anyway, aside from all that (from Doctor Vic :-)), this is one of the more useful articles I've just found amidst the morass online about writer's block and such. Indeed, I'm bookmarking it for myself too, as I've got too far away from my writing life, and need to get it back!!!
Writer's Block: Is It All in Your Head?
Blessings to ya,
Vic