Dear Jane, My sister died in a car accident in January of 1989. I was 18 at the time of my sister's death, never received any counseling and went on to finish college. My problem now is fear of death. I'm really not into support groups or psychiatrists. Yes, this is normal.
Many people experience death anxiety after the sudden loss of a loved one.
Sometimes, as in your case, this anxiety occurs many years later. This usually happens when someone gets back into life very quickly and doesn't have the time to process their feelings of loss. There are many good books written about sibling loss. This might be an avenue of exploration for you. Of course, I feel most people achieve more benefits quicker by reading and attending counseling.