We touched on this in class today very briefly, and my professor mentioned that there was a very long (300 years) debate about whether Jesus should be worshiped, or if he should be treated in a similar fashion as Muhammad, who is considered strictly a prophet.
Please recognize your Christian bias. Jesus is still seen as "just a prophet" in Islam. Wikipedia also has a lot of the evolution of Jesus worship in various christian religions.
Your question likely touches on some of the most key and formative debates in Christianity, on the nature of Christ. Early contenders include Monophysitism which says that the nature of Christ is entirely or overwhelmingly divine, Nestorianism wherein his nature is (primarily) human, or Arianism, in which Christ has divine and human natures, but is created by God as opposed to being an aspect of God. [all of the above are extreme simplifications to fit into one sentence, or course]
Orthodox Christianity as defined by the council of Nicea, says that Christ is fully human and fully divine, and was "begotten not made", ie is not subordinate to God This is the view that won out pretty much everywhere except for a few Nestorian remnants, and the Coptic church, which is monophysite.
I suspect that your teacher was referring to the period during which all this was being hashed out, which was roughly the 200's to the 500's, and being imprecise in terminology about whether Jesus should be "worshiped"