Does this sound like synesthesia?

Yes. You don't need to actually see the colors for it to be synesthesia. There are two broad categories of synesthesia - projected and associated. People with projected synesthesia see the colors in their field of vision. People with associated synesthesia see the colors in their mind's eye. Associated is much more common; both types are equally valid. As long as your color associations are involuntary and consistent, you have synesthesia.