Hi Betty,
The first thing I would do is talk to the hospital social worker or local American Cancer Society office and find a caregivers support group for yourself. Treatment is very hard and caregiving even harder. She may lash out at you just because you the the closest person nearby so if you are thin-skinned you may have problems dealing with this. I was pretty tough on my loving wife/caregiver during the worst part of my treatment. I was pissed off about everything.
Seeing your own immortality as mirrored by your sister is tough also - I had some friends who just couldn't cope with it. That's why counseling and a support group are invaluable.

Suicidal thoughts and depression are normal byproducts of this disease. If she starts talking about a method of suicide or disposition of her assets (like who gets what), seek immediate help from suicide prevention. It is good that she has gotten medication for depression - most of us need it and it should help a lot.

You mentioned she hasn't started radiation yet? Many consider the surgery to be the easy part. Does she have a PEG tube?

Your willingness to walk along side her tells me that you won't let her down. The medical team has the primary responsibility for her care so don't be over-responsible either.

If you are going to be a caregiver then go to the appointments with her and take notes whenever possible. We are always here to help with any other questions you may have.

The medical team you will be interfacing with will typically have an:

-Oncologist (chemo and usually the primary care doctor)- Usually the oncologist will manage and coordinate all of the prescriptions also, such as pain medications, anti-depression medications, constipation meds, etc.
-Radiation Oncologist - plans and administers radiation therapy
-Head and Neck surgeon (sometimes ENT) will have primary responsibility for surgical aspects and post treatment recurrence surveillance or followup.
-Nutritionist - deals with dietary issues
-Oncology advice nurse- for dealing with day-to-day issues.

There will be many others involved but these are the important ones.

My wife gave me a book called "Living Well With Cancer" by Katen Moore and that helped a lot to take the mystery out of it. You can order it through the link below or choose from other books that are on the OCF booklist http://www.oralcancerfoundation.org/products/books.htm