Hopefully I get a compassionate case worker that understands that I don't want to ruin my body/health over a job and possibly become bigger burden on society when they ask me why I quit this job.

I'm afraid the empathy of the UC adjudicator doesn't matter one whit. This will be a straight-forward issue under your State's UC statutes. You most certainly shold apply for unemployment benefits and see what happens - you have nothing to lose by doing so.

Good luck with the job search.