Only you can know.
Here are some elements you may want to consider.
A PhD is at least 3 long years. Do you think your girlfriend may be able to join you there at a moment? Do you think your relationship is strong enough to survive this trial ?
A PhD can be very difficult. I personnaly failed, as I felt too lonely and had low self esteem.
On the other hand, my friends who succeeded in getting a PhD now have very stable position. I even know a friend who did his PhD in belgium whil his girlfriend did hers in New-York. They live happily together now.
As for your parents, do not worry. You have a full life to live, if you show them love and affection from abroad, if you come and see them when your finances allow you, they shall be proud of your determination.
Last : weigh rationnally all the pros and cons, but chose with your heart. I mean it. Do as you rally feel, and it will be alright.
Mgoussu Michel, Ruined a lot of relationships. Learned from this, books, and others.
Source: Quora Digest