Whats your computer experience like, did you do any C++ coding?
A strong physics / maths background and a good coding level should get you a coding job.
Game design is a much trickier field to get into. You can get some experience for it by doing levels for games like unreal / half-life / counterstrike / etc… and try get some recognition from that.
Other ways of getting into design is from a testing job in a company and branching to a new field from within the company.