I took a philosophy class that was based around watching historical movies, and Elizabeth was one of them...so here's my take.
I think one of the big reasons Red is a prominent color in the movie is because of how Elizabeth came to be Queen - Mary was an absolute butcher, killing Protestants left, right and center (maybe not THAT bad, but check it up historically), wasn't she called Bloody Mary? Anyway I think like Sam said, the color red indicates not only bloodshed, but conflict and a 'state of war'. Elizabeth took the throne at a very precarious time, and had to navigate several religious and political factions against one another to stay on top.
Does your teacher mention contrasting red, white and black? I think that's pretty crucial too: black, in many cases, means secrecy/mystery, which pretty accurately describes the political intrigues of Elizabethan England. So to me black/shadows in the movie represent the secrecy, deceit and manipulating (mostly with Wolsingham?) that went on to take down Elizabeth / keep her on the throne.
White often is meant to represent purity, almost to a holy level. This obviously is meant to represent Elizabeth as the Virgin Queen - whether she was actually a virgin is irrelevant - the most important thing is her oath/pledge/commitment to her country and people to be wed to THEM, and to no one else. I think in the movie Elizabeth is portrayed as having very human flaws, and she realizes she can't fulfill her duty to her country and people if she is focused/distracted by men, or "temptations of the flesh". To combat this she pledges to never wed any man, and remains pure for England. This not only makes her focused on ruling her nation, but MOST importantly it gives her an "aura" - makes her more divine/holy than anyone else - this is critical for a woman ruling in such a chaotic time IMO, because she needs to be seen as a symbol, and not as a woman.
Uh, end/rant. Make sense at all?