Is it possible for me to have syringomyelia even though i'm young and healthy?

Yes: A spinal syrinx (hole of fluid within the spinal cord) can be a distant result of a previous spinal cord trauma. But if you do have a spinal cord syrinx, it is important to assure that you do not have several of the causes of syrinx, including chiari malformation, spinal cord tumors, etc. Please see your doctor for full workup (to include spinal mri's with contrast).