If this helps- my gym has a membership plan that is only $10 a month and they have showers at the gym.... I know its not a long term solution, but you may not find a magic bullet that fixes all your problems at once, you may have to find one solution at a time.
Seriously, get a job. I am 32 and since I got my working papers at 15 I've never not had a job. Even if it was bussing tables, or doing someone else's laundry, or sweeping up at the local hair salon. I am not telling you to commit fraud, but I've had a lot of cash jobs that were off the books. Mow lawns, rake leaves, split firewood, shovel snow, get a freekin paper route. Knock on your neighbor's doors or put a note in their mail boxes to see if they need help with the yard, or moving furniture, cleaning out the attic, whatever. I've gotten a lot of jobs just walking into places- Deli's, laundrymats, hair salons, restaurants etc and asking if they are hiring. PS. if you are going to try that, wear pants that fit. Make a good first impression.