We didnt have a washing machine when I first moved out- washed clothes in the shower/bath and used a clothes drying rack. Yes it's not as easy, but it's very doable, esp for smaller things. People survived without washing machines for thousands of years-just a thought.
I don't think anyone here knows your situation, so just ignore the judgement and do what is best for you- I think that mental health is 1000000x more important than an extra 10% savings. Maybe without the anxiety that the living situation brings, you'll be in a better place to trim other budget areas (when I'm stressed, I eat much worse than usual, shop more, pay for stupidly expensive yoga classes etc). Good luck! Xo