Hang in there!
In the summer of 2010, I was in almost the same position (21 years old with a 2 month-old son and a failed relationship). It wasn’t until about 7 or 8 months of sending out resumes and portfolios (and I was STILL working part time at a pizza shop) that I realized I needed to treat my situation more like a design challenge. The constraints were pretty clear - money, time, and level of comfort. I sold everything and moved to NYC with a some clothes, a sketchbook, and a suit. A few uncomfortable months later, I had landed the first gig at a job fair. That was all I needed - I figured any design job couldn’t be as hard as designing your own (and your kid’s) future. So far, so good.
But those “uncomfortable months” were easily the worst months of my life. If I could give any advice besides “keep at it,” I would suggest to
A) Don’t stagnate! Keep learning/ designing/ networking. TONS of free and cheap resources online. Learn something to stand out as an ID candidate (Javascript? Experimental photography? Basic UI/UX principles?)
B) Follow your passions. Cheesy I know, but easy to forget about in this scary period.
I wouldn’t have stood a chance without the help (and couches) of friends and the mini projects I gave myself - usually design competitions. Following my passions led to me explore with a more optimistic view, and allowed me to network outside of the design world, which really led to a more lasting impression than my name on a business card.
Good luck!