I've done that before, but since I work 30 minutes (minimum) from work, I was a lot later than you.

Remember to cut yourself some slack... your body is going to need rest and will claim it for itself when we don't do it ourselves. If your brain was racing last night, you couldn't rest, and once it shut down your body took it's down time. You are under a lot of stress, especially with your father's condition, so it is to be expected. Realise that if you don't give yourself that time to crash when you can, you may find yourself extremely ill/sick and having to take down time.
I'm hoping that your boss is understanding of your situation and that you had no reprecussions for coming in late. I'm amazed that you were only 45 minutes late, especially with all that you've been putting yourself through lately. You should be commended on going ahead and getting in to work and only being 45 minutes late. I work with a lot of folks who would have just blown off the day after a start like that.
Prayers continuing for your family, and especially your dad. Be careful on that long drive, and be sure you get as much rest as you can before driving!
Oh... and btw... I was 2 hours late for work this morning myself. Woke up with a migraine, called bossie and told him I was taking meds and going back to sleep for an hour or two to get it under control before coming in. So I'm right there with you today!