Given that Oedipus' character (from Sophocles' play "Oedipus Rex") was critically examined by Aristotle in his text Poetics, one could make an argument that Oedipus does not fit perfectly into the definition of Shakespeare's typical tragic hero.
While Oedipus does possess a tragic flaw (or hamartia as defined by Aristotle), one could argue that Oedipus does not hold up, characteristically, to what is expected of a modern true tragic hero.
To do this, one would need to look at the characteristics of both Aristotle's and Shakespeare's tragic hero.
According to Aristotle, a tragic hero must possess the following ideals/characteristics: noble statue and possess greatness, occupy a high position and embody virtue, be considered great (but not perfect), the downfall is the fault of the hero, misfortune is not completely brought about by their own actions, their fall increases self-discovery, the hero's fall does not leave the audience (or reader) depressed.
According to Shakespeare, a tragic hero must possess the following ideals/characteristics: downfall due to pride, doomed from the start, typically a leader (or king), suffering must be for a reason, tragic hero is typically male.
In order to prove your thesis, examine and support the textual evidence which proves Oedipus to not adhere to the tragic hero characteristics.
Another thesis you could develop is how the environment which surrounded Oedipus had more influence over his actions than his own decisions. Basically, you would be looking at the concept of nature verses nurture.