You CAN go on--just not the way you've BEEN going on. The way it's been has taken a great toll on you. Sometimes sheer exhaustion is your best friend. It's your body/mind telling you ENOUGH.
This is the time for extreme prioritization. I did that when I had my surgery. I got everything in place that I needed to, and then just plain put myself first for a couple of weeks. I asked for help from friends and family. I let people do things for me. My sweet neighbor came over yesterday to collect my bag of trash and put the already-full trash can out for collection this morning. They stop by every day to see if I need anything. I was debating working part time this week, but the disability issues were complicated enough I decided, "screw it, I'm taking the time I need till I feel completely up to working." Just sent the form to my doc to certify my disability through this week (my original projected return to work was determined before I had to be re-admitted to the hospital for several more days with an extremely uncomfortable complication). I need the time, I'm entitled to it, so I'm taking it.
You have to do something similar. Make yourself number one for a while.