I think you need to focus on your priorities here. As I understand you're currently jobless and obviously have no health benefits, and are on the verge of becoming homeless. Doing three months of "intense manual labor" to get a paycheck and health benefits is (in my view at least) far preferable to being homeless and penniless.
My perception of your reply is that you think the Amazon warehouse job is beneath you; does homelessness appeal more? Seriously, at this stage, in the very short run, your number one priority should be to avert homelessness, and do whatever it takes. I know you mentioned back pain, but if the Amazon warehouse isn't your thing, there should be something else you can do to tide you over.
More broadly as lot of commenters have very kindly offered to talk to you and help you in various ways. That is an immense gift! Make use of it, and don't make them regret offering their assistance.
You're in a bad place mentally right now, but you're young, you're not stupid and you can get out of this, but you need to be willing to put in the effort. Asking the question here is a very good first step.
Lastly, you may also want to visit Ask A Manager [1] which has a lot of good advice on cover letters, resumes, interviewing, etc. It's not tech-specific, but most of the advice applies universally.
Good luck!
I won't lie and say it was as fun as traditional programming. But QA means a lot of different things, and just because you had a really bad experience with it (and I've heard terrible things about EA in general, not just their QA department), you should definitely be looking at QA for job opportunities that will meet your needs. Realistically you're going to be better suited to a lot of QA jobs right now, and employers are going to be more open to taking a chance on you given your history.
More senior qa roles will be designing test suites, maybe even developing them, but entry level game QA is not going to scratch a dev itch.
This isn’t true? https://www.aboutamazon.com/news/operations/healthcare-from-...
Instacart (in some locations) allows you to sign up just to do the shopping (then the drivers pick it up).
Taskrabbit will definitely have some things you can do without driving as well.
Just explore the options; something where you can set your own schedule would be really nice while you're job hunting and interviewing.