Whether you will stay in Turkey or move back home--or move somewhere else, for that matter--is entirely your choice. It isn't fated at all. There might be transits coming up in the next few years that will make one or another of those choices more desirable, but I'm not knowledgeable enough about transits to be able to say what they are. And even if those kinds of transits do occur, you will still have a choice, and you'll arrive at it based on whatever is happening in your life.
Astral transits might have some influence on what kinds of things happen in your life when, but they don't determine how what's going on in your life will respond to their energies. Just like if it rains on your wedding day, and you had planned to have an outdoor wedding, that influences your decision, but the formation of rainclouds didn't make it your fate to get married indoors. You could just as easily decide to hold your wedding during the dry season instead, or get married outdoors anyway and get your whole wedding party soaking wet (would make for some unique wedding memories!).
However, what pictures your birth chart shows indicate the kinds of interests you have and the kind of life path you are inclined to take. Any choices you make in regard to those things are always in keeping with your natal chart, even if you've never heard of astrology. If you respond to your natal chart in an authentic way, in keeping with who you are, you will have a good life. In the case of a career, to have a successful career that makes you happy, it has to be something in keeping with what your authentic self wants, and your birth chart will reflect this. Yours shows that getting a PhD in art history is the kind of thing that you're authentically inclined to do, so yes, in that way, you're on the right track. And if you didn't pursue that art history PhD, you would do something else that reflects those same energies, just in a different way.
You have a strong planetary concentration--sun, moon, Mars, and Venus--in the second house, with each of them forming conjunctions with at least three of the others. That means you have a strong focus on your sense of self, on developing your own values and your own place in the world. Second house is also associated with money, so making money might be very important to you, too, and with the body, so with a strong concentration there, you might be especially conscious of your health and/or body image.
Your sun is in Libra right on the cusp of Virgo. A Libra sun indicates a personality that needs to grow itself through seeking balance, harmony, beauty, justice, connection with others, any or all of those things. Being on the cusp of Virgo, it's also motivated by Virgo's message, which is to develop the self through your life's work. Adding to the beauty/harmony message is your Venus in Libra conjunct your sun.
It's no accident that you want a career in art history. That satisfies your Libra sun/Venus imperative for seeking beauty and your Virgo imperative for making it your life's work. You also have Mars conjunct your sun in Virgo, indicating that you need your life's work to be something you're passionate about, and the moon in conjunction with Mars and the sun, also in Virgo. Moon signifies your deepest desires... what your soul wants. And your soul also wants that growth through work that you're passionate about.
I also see Saturn in Sagittarius. Sagittarius is the sign of the lifelong learner... its archetypes include the student, the philosopher, and the gypsy... and Saturn is self discipline at its best. No accident that you're going for a PhD. You have a desire to learn coupled with the discipline to achieve. That's exactly the type of person who becomes a PhD candidate. And you have Uranus conjunct Saturn, also in Sag. Uranus is about uniqueness, breaking the usual social norms, going against the grain. Your Sagittarian desire for learning and your Saturnian discipline are conjoined with a desire to make that learning about something unique and different and off the beaten path, and art history fits the bill.
Then you have Jupiter in the ninth house. Jupiter is the planet of expansion, and the ninth house is its native house. Both of them are associated with education and travel and expanding the mind. Since your Jupiter is what astrologers call a singleton--it's all alone in that upper hemisphere of your chart--it has a much stronger influence, all by itself, on your psyche than it would if it had more close neighbors. No accident that you moved abroad for love and studies. That's a thoroughly ninth-house-Jupiter kind of experience. And your Jupiter is in Aries, which is the sign of pure will pushing to expand itself. It's also near the cusp of Taurus, which is a grounding earth sign and also has associations with art, beauty, and love, so again, no accident that art and love influenced your Jupiter choices.
You've done all of these things in keeping with your birth chart without even knowing that they were in keeping with your birth chart. That says you not only are on the right path, you instinctively know what that right path is. So keep doing what you're doing, and when you're faced with choices, make them however you've been making them.