The thing is that I made the account in Qatar, so it must have registered the country as Qatar automatically, but I have a Turkish citizenship and passport. I was living in Qatar, but I am originally from Turkey, can the country still be changed?
I'm afraid not, with the current system it only counts the country you're logging in from. If you were to login from turkey for the duration, it would give you the option to switch to turkey, but otherwise no.
You could use a VPN, but I should point out that forgetting to use the VPN once will reset your progress towards flag change.
I'm currently living in Turkey right now, but when I registered my account I was in Qatar, would it still be possible for my country to be changed to Turkey?
Oh I misread I guess, if you are curretly living in turkey then yes, it will count towards the change timer and after a couple months you will get the option to switch your flag to turkey.