Teiresias is, indeed, the one who knew from the start that Oedipus was the cause of the plague on Thebes. Teiresias does not want to tell Oedipus for fear that it will bring Oedipus great shame and harm.
It is ironic that Teiresias is the one who knows of the cause of the plague because Teiresias is physically blind, yet he can "see" the cause of the problems around him. Oedipus can physically see but is blind to the cause of the problems that surround him (when he, the cause of them problems, should know better than anyone).
Teiresias is, whenever he appears in Greek literature (and particularly in Greek drama) blessed with the skill of prophecy and foresight. He is blind (the symbolism usually being that - without eyes, and after suffering - one becomes wiser. Without eyes, you can see more than the world... you can see beyond time) and he is led by a little boy, usually, another symbol of his unusual relationship with between young/old, future/past.
Teiresias knows, and tells Oedipus, the truth. Oedipus asks him to name the murderer responsible for the plague (it's Oedipus!) and he refuses. Teiresias tells him that even his words “miss the mark”, and, to everyone present, announces “All of you here know nothing,”.
Teiresias then tells Oedipus that he himself is the cause of the plague. Oedipus doesn't believe Teiresias, calling him “blind in mind and ears / as well as in your eyes”. Why is this an ironic way for Oedipus to respond? Because Teiresias is right, and, as he goes on to say, the insults Oedipus heaps upon him will, before the play is over, be true of Oedipus himself. He will end up with everything he now thinks he "knows" in tatters: and, like Teiresias, he will end up able to see more clearly into the future (as he does in Oedipus at Colonos) and - with horrible irony - like, Teiresias, blind.
Hope it helps!