You aren’t necessarily stuck there with no days off for the next 10 months. Perhaps your supervisor would be amenable to you taking unpaid time off. It’s a reasonable request given that your time off for family obligations was not “vacation.” You wouldn’t be asking for them to pay you for more time–just to let you get a much-needed day off or brief vacation, without pay.
That sucks Otto. I’m looking forward to a job that uses PTO instead of vacation and sick days because I rarely get sick so it means more vacation for me but now I know there is a potential downside. Of course, with switching jobs, I’m not eligible to take any vacation for 6 months but then I get a year’s worth in the last 4 months. Hope things start getting better for you.