1)The main source for the "trojan war" is the "Illiad" told by the poet Homer,he wasn't even a historian.
2)All stuff about Troy is only in greek mythology,not history,therefore all characters there(including the greek leaders) didn't exist in real life.
3)If I'm not mistaken the story ends with Troy being completely destroyed and the possible remaining trojans fleeing Anatolia for good.
Now based on real history the greeks managed to make greek cities in Anatolia and conquer and convert anatolian people to hellenism,and at least 2-3 major hellenic empires ruled the area long before any turko-mong's horse stomped on that land.
I'd say the chances favor greatly of you being some greek descendant rather than a trojan,whatever that means.
Define almost,by your logic half of Germany should be feeling polish right now,whole of the Americas should be feeling amerindian,most of Japan should be feeling Ainu, the people living in Great Britain should be all homogenous etc. etc. I'd say it's the other way you just describe it.