First, congratulations on being a new mom, but I'm so sorry to hear about your son's health issues. It can be difficult enough handling life with a new baby (I remember too well) without the added stress of money and health issues.
Since it sounds like you're on the move frequently, you'll want to find a WFH job with a flexible schedule. If you haven't already checked it out, The Penny Hoarder has a WFH job portal (https://www.thepennyhoarder.com/wfh/) where you can immediately see whether the job offers a flexible schedule (look for a clock icon next to the listing). Also, we recently published a list of 10 side gigs for stay-at-home parents — maybe it could give you some ideas: https://www.thepennyhoarder.co...stay-at-home-parent/.
And here's the thing that I learned as a mom who worked from home for much of her daughter's first five years: There's a window of time early on when it's easier to work from home because the baby isn't mobile. Once your child reaches crawling and walking stages, the WFH life becomes much more challenging. (The good news is that once children become more independent, it becomes easier to manage a WFH schedule again.) If you establish a routine now, you'll be better equipped to handle the challenges to come.
Also, you mentioned that the medical bills were piling up. Don't be afraid to reach out to medical providers to negotiate payment plans and other options (we have an article about that, too:https://www.thepennyhoarder.com/debt/medical-debt/). I know it seems like just another thing to add to the long list of things to do, but it could be worth your effort if it means you can stress a little less about money and enjoy more time with your son. It goes by fast.