Harris is generally considered to mean "son of Harry." The given name Harry is a derivation of Henry, meaning "home ruler." Like many patronymic surnames, the surnames HARRIS and HARRISON are often found used inter-changeably in early records - sometimes with the same family.
Harris has origins in both England (yes English is a possibility) but Harris is also within Welsh as well, so you could have Welsh.
I recommend knowing your ancestors names and look through the census (Look at the one who arrives over to America and where they may have landed.) There are immigration records that they do post-arrival to America, along with census to check out for.
"In fear I hurried this way and that. I had the taste of blood and chocolate in my mouth, the one as hateful as the other."Hermann Hesse, Steppenwolf