Game programming after computer engineering help!

Hi guys. I am about to finish Computer Engeenering college, but I want to be a game programmer. I will finish my 3rd year of college as computer engeener and I want to know if I am to late to study game programming. I am 22-23 years old now, is it too old to start over again and to learn game programming? Also can i take master in computer science after finishing computer engeenering college...
Please answer my questions, thanks!