As stated twice above, cancer is not contagious.
If your family friend was in the hospital, the first thing that would have been done is a blood draw to rule out many problems. Hospitals have incredibly high tech equipement which can detect blood disorders very rapidly.
As for her blood getting on you, HIV is an extremely fragile virus and immediate exposure to air will kill it. Which is why you are only at risk if the virus is passed inside the body. You had no risk.
I have worked around AIDS patients for years and have had every imaginable bodily fluid splashed on me, into my eyes and mouth and have had numerous needle sticks and I don't have it. We say here often that knowledge is power and it's the truth. Get yourself educated about HIV/AIDS and you'll be much less anxious.
I hope your friend will be fine and out of the hospital soon.
Peace
Greenlydia
Agree with mammo. Will just repeat in another way to reassure you.
Since the publicity about AIDs started over 20 yrs ago, it is common to be fearful of catching the virus by exposure to blood. I am guessing your real fear when you say 'other things' is AIDs.
Cancer is not contagious. So no worries on that front.
AIDs can only be passed if your friend has it, and it got into an open cut on your hand.
I can't think of anything you should be worried about, but do see your doctor if fears increase or don't abate. Focus on giving love to your friend.
Unless your friend has AIDS, or Hepatitis and her blood touched an open area on your skin like a scartch, you have nothing to worry about. You can't get cancer this way.