You should be able to play most games at medium quality @ 1600x900 with a nVidia GT 550M. However, I recommend getting a GT 555M if possible.
I have a nVidia GT 550M in my laptop with 1366x768 resolution and I think it's perfectly fine for it with medium quality graphic settings. 1600x900 represents a 37% increase in the total number of pixels. Graphics card performance is directly related to the resolution, so the higher the resolution the lower the performance.
I tested Crysis on my Lenovo Y470 laptop with medium quality settings and AA x2. I used 2nd chapter of Crysis, Relic, to measure frame rates where were as follows:
Peak frame rates = 55 FPS
90% of the time frame rates ranged between 31 FPS to 45 FPS
Lowest dip = 17 FPS.
Since a 1600x900 resolution screen has 37% more pixels to push, the FPS would drop by at least 37%. Therefore, the estimated frame rates would be as follows (or perhaps a little lower):
Peak frame rates = 35 FPS
90% of the time frame rates ranged between 20 FPS to 28 FPS
Lowest dip = 11 FPS.