Hi Muffy,
My husband is also very independent and private and told only our closest family and a friend at first. I stayed with him in the hospital and would do the same for anyone who asked me to stay by their side through this fight. The nurses were really open and mind but they have many patients to see, so I was of help in critical and unpleasant situations for my husbands every need.( His case is different in that he had a trachea but you will also need help for all sorts of needs)
Even if its just for the emotional support, you should have a team of helpers on a rotating schedule or people that can be assigned to different tasks. For example, making all those calls and all the research is more than a full time job. Cooking puree soups and saucy meals that are high in nutrients and easy to swallow.
As a teacher the first people that will guide you through dealing with a medical/sick leave is your 'Union'.
Your doctor will also send a sick leave note to the principal at your school and he will forward that sick leave to your employer, your district office 'human resources'.
You are under no obligation to explain why you are sick, but you may say that you are undergoing a medical emergency or simply that your doctor put you off of work for medical reasons.
If you have accumulated unused sick time, you should be able to use it all up. Some teachers have a year or more accumulated and this insures no break in their pay. You may even be able to borrow a few weeks from next year if you run out of you sick days.
If your teacher's union requires all teacher's to be part of a 'group insurance' than you would want to contact them and see what you are covered for. I know in the case of my insurance they would want to be notified within a certain time, EG: a month. Otherwise there might be 'employment Insurance' benefits for long term leaves, and it is worth giving them a call later on when life slows down again because they may have some kind of specialized funding. I know in Canada, you can apply for your pension plan if you payed into it and you are between the ages of 18 and 65.
You are in my thoughts, Sophie