juggle - To keep several objects in motion in the air at the same time; or to try to deal with two or more important jobs or activities at the same time

It wasn't easy for Beth to juggle working at her job from home and taking care of her kids when they came home from school.
frazzled - To feel completely exhausted and worn out, and unable to think straight, after a great deal of mental or physical effort
After being up two nights in a row writing a 60 page history paper, and drinking 60 cups of coffee, Simon's mind felt frazzled.