I am in the same boat as you. Young grad student, limited budget etc... you all know the story. What I have found is, depending on your interest, find overseas opportunities that fit with what you are looking to do. They not only help build your international network, but also give you strong learning experiences to use once you graduate. If the program is organized by the school jump on it. Chances are they will pay your way through scholarships or other funding.
This year I am on my third trip to China right now. All paid, except for maybe 20% of the cost. I have two more trips to India planned for the rest of the year, again paid. School programs primarily, but all fundable through the University. They will give you money if you position yourself right.
What this equates to. Great experiences, seeing the world, and TONS of miles. I will have Exec Plat on UA as a result, and will paid a pretty minimal fee for it.
I definitely agree with what has been said. Keep you expenses to a minimum, but make use other opportunities to help you see your girlfriend frequently, at a minimal cost.
Hope this helps.