I started the beginners program today, so I am very new to all of this. I can't help but feel discouraged though. As a teenager I had cancer and the doctors concluded that the radiation affected some development in my neck. Everything functions as normal except for the fact that I can't lift my head off the floor at all and can't keep it in the air without hand support.

How I can go about working around this?

Moralize much of this work can be done with while the head lies flat on the floor ( with no elevation ) and also head support can be used while lying down on the mat !

Peak Pilates makes a wedge that can be used to prop up the head/shoulders to do the mat work. It is a bit expensive but maybe you can find something similar to use that is less expensive. Here is a link http://peakpilates.com/flex-cushion