Sorry, Mpolat, I'm replying without an answer but just wanted to say that you are not alone in that boat. I have no idea on my chances to be admitted by Georgetown. I am an Arab living in the US and also applying to the Arab & Islamic studies of which the deadline is too close, Dec 15! I finished Arabic classes, along with others, in an Islamic seminary but the problem is that the learning system there is unofficial that they do not provide transcripts. I don't know if my high grades in Arabic in high school is counted (or even reportable).
Your GRE scores are better than mine but I don't have to take TOEFL as I have a master of public policy from an English-speaking institution with a 3.7 GPA. According to their website, Georgetown mentions that there is no minimum GRE score as they consider the whole application as there may be strengths that make up for the low GRE scores, although I am not sure how that would work. Hope somebody from Georgetown can address our concerns.