Hiya Jaci,
Don't be so hard on yourself. Situations like this are bound to create high anxiety and panic. And it is ok for people at your work to help you out. I am sure if they do that it is because they like you because you are a good person. And it's ok in extreme moments to have the help of those who like us. As for your family, the best you can do for them is take good care of yourself, be patient for yourself and just take care of your anxiety until you are ready to spend time with your dad. Anyway, I wish you all the best, I know what you are going through, my dad has been fighting his cancer for 6 years now. Hang in there and my prayers go out to you and your family.
-Diva