you don't "need" any particular focal length, but there are pro/cons (aka differences) between any two focal lengths.
assuming both the 55mm and 85mm are 1.8 -- similarly frame, the 85mm will add a lot more compression and will more than likely provide a subjectively more pleasant background.
at the same time, if you actually want to provide more of the environment in your image, it's going to be harder to do at 85mm where you will have to back-up significantly away from the subject.
I tend to use my 58mm for general portraits where I want to include the environment. I'll swap it for my 85mm or 70-200, when I want a tighter frame and eliminate the BG from the image.
If you're shooting head-shots, not full body, it's generally better to use a longer lens for a number of factors.