We all get 10 days of paid vacation and 10 holidays throughout the year. That’s typical stuff.
We also get five days of Personal Time Off (PTO). You can take time off for any reason or no reason at all. Just let the rest of us know, “taking PTO tomorrow morning.” Mostly these are used for personal appointments, child care, extensive car repairs, etc.
In practice, nobody keeps track of your time, except you. But everybody in your team will implicitly keep track your results, simply because they depend on you as you depend on them.
BTW, if you have a family emergency, go take care of your family. Take whatever time you need. We’ll worry about the formalities later.
Please, read about the context for these answers.