Does anyone else get really frustrated at the Ellis Island.org website?

I know my great grandma went through there...but I can't find her on the records. My grandma said that she went through in 1916 although she was not entirely certain. Her name is Johanna Patricia Cantillon or Patricia Johanna Cantillon (she went by both). When she was in America she went by Hanna as well so maybe thats it... The website says no Cantillon has ever gone through there, but then sometimes it does say Cantillons have gone through there but shes not listed. Please someone help me find her. She was born on March 15, 1901. Ancestry.com also doesn't have her immigration. This website is really messing with my head, I really want to find my great grandma.