After you receive a PhD, people will look at what field your research was in, who you worked with, and what papers you published. You can do "medical physics" work through a biology department, a physics department, an engineering dept,etc, as well a special interdisciplinary program (probably built with faculty from several deparmtnets rather than being it's own department), etc. Your degree could therefore be a "Doctorate in Boilogy" a "Doctorate in Physics" perhaps have some special "Medical Physics certification", etc... but what should matter most is not what your degree says, but what you did to get the degree... that influences what you do later in life.
That said, most grad programs have "core" courses that need to be completed, as well as various preliminary and comprehensive exams... and your selection of a department/program effects THOSE.
It's too late to apply now... but did you consider Md/PhD programs?
Have you been accepted to any programs in Medical Physics? Or any other programs in physics or bio, etc.?