I would make yourself more useful at your mom's and offer to go/help with the grocery shopping and food prep (learn to cook simple meals); do the dishes after meals and practice being reliable, showing up and being there, chatting with your mom, keeping your room neat/clean and your laundry done (and the household's, there's beds to change and sheets, towels and dish towels to wash) and the bathroom picked up, etc. You do not have to act like a burden and if you don't act like a burden, you won't feel like one?

Maybe make yourself a schedule and don't hang at your friend's so much? Your friend and/or his mom may not be so keen on that and/or if you are there, your friend may not be working on some things s/he should be to care adequately for him/herself? If you are out and about, shopping and learning to do stuff to run a household, it's more likely you might meet someone or see jobs available that might interest you. Notice which of your mom's neighbors are older and see if you can't do chores for them for a few bucks here and there if they want to pay you; it's good practice talking to people and becoming more comfortable around all sorts. You could start a small dog sitting/walking service or house watching for when people go on vacation, etc. Make a little brochure and go door-to-door in a block area/apartment building and introduce yourself and just be friendly and chat with people if they want.

When you don't have to go to a set job, that's the time to look around and try a whole bunch of things. Volunteer for several places; think about delivering pizza or business-to-business packages or starting an errand running service. Find an old yellow pages phone book and leaf through it looking at all the jobs and see if any ideas jump out at you. See if you can get a janitorial/cleaning/helper types of jobs for small businesses. Insurance agents and Realtors all work for themselves, find "tiny" businesses like that who have offices and see if you can figure out how to get a little money from several. Go "underground" until you can figure out what you'd like to do, save some of what little you make so you'll have a little savings in a year or two to make a start once you get a "real" job you like.