Life happens to all of us and sometimes you have to take time away that you were not planning for. In the interest of "putting my money where my mouth is" I'll share that this week I have been feeling quite under the weather, and have spent a lot of time trying to convince myself that rest, and not "working through it" was the solution. I thought I would share some of the strategies I used to feel "in control" of the situation while still taking time for myself, as many of these strategies aren't widely broadcast.
Use a vacation responder.
A short message sent automatically in response can help temper expectations about when you'll be able to return messages without putting the onus on you to respond right away. My text says:
Thank you for your email. I am away from my computer with limited access to email, and may be responding to emails more slowly than normal. I expect to return on {date} and will do my best to respond promptly at that time.
If I were teaching or involved in something time sensitive, I might include language about who else to contact like:
If this is a time-sensitive or urgent matter about {insert course name or project here}, please contact {name} and {email}.
Knowing that my emails are handled lets me rest a little, and alleviates some of the anxiety I feel when I know I'm not responding to emails like I should be.
Move meetings to virtual spaces / over email if possible.
Skype/Google Hangouts/Zoom and other technologies all make it possible for you to keep your commitments without necessary committing to being in a physical space. I have met with my advisor, with students in office hours, and with collaborators on a variety of projects over Skype. I have also offered to send my thoughts for a meeting over email, or tasked a fellow grad student to attend a meeting in my place. It isn't ideal but it can help to show that you're dedicated to moving a project forward even if you can't commit the physical/emotional energy to being in that space physically. Just make sure that you've done the "professional check" and that you're Skyping in an outfit/from a location that makes you feel comfortable.
Communicate changes in deadlines before they pass.
Perhaps the worst feeling when dealing with unexpected circumstances is my divided attention. It is hard to have your attention split between what you unexpectedly need to be doing, and what you were planning to do before the circumstances arose. Clear your schedule, and change the deadlines you need to before you miss them. An email with a heads up, and a tentative new deadline, can do a lot to remedy the guilt and anxiety of not being sure if you will make the original deadline and make you look professional and on top of things to boot.
Once the decks are cleared, actually rest/be present where you need to be.
Once you've let the appropriate people know and made arrangements for your absence, actually rest and disconnect. Seeing more senior people in my department and other contexts deal with life's unexpected events in professional ways that still maintain privacy was my biggest signal that it was okay for me to do the same. So model it for your colleagues, your students, and even up the chain, to make these social graces the norm and not the exception.