You're not a burden on anyone. You're still really new and in a strange world; otherworlders are supposed to help each other out, and the locals wanna help out too, that's why there's the Welcome Center and the apartments that are free for a few months.

If you want, I bet the farmers outside the city could use a hand, especially right now. And there's always the Task Board if you wanna help someone out short-term and make some quick cash that way.