Georgie, Sometimes it's difficult to explain what is going on when one says they can feel but cant make the affected muscle work. My accident happened 45 years ago and many medical procedures have changed over this long time, but unfortunately not much in the way of a cure for nerve damage, if this is what has happened. What does concern me is what you posted, that she says she can't cough or lift a glass to her lips. I don't know where she had the vertebrectomy, at what level, and this might help in understanding where her problem is. If the vertebrectomy was low, for example in the small of her back, say the T-12 level, then this area if there was nerve damage, wouldn't affect her arms or hands or lungs. As far as having pain when touched, this too is a possibility. I had two vertebrae crushed at the T-11 and T-12 level which required a vertebrectomy and laminaectomy of several others. I had true spinal cord damage, but it was incomplete. I had feeling in some parts and others places when I was touched I would just scream in pain. If you ever had an arm go to sleep then have a feeling of electricity kind of, this is similar to what i had but magnify the feeling by a factor of 10.
Although she may have feeling but she says her legs feel heavy is probably true. It takes a signal through the nerves to the muscles to make them work, but if that signal is there but it is not strong, it could make her legs feel heavy. I am no physician but only rely on experience, but to me it sounds like it's a possibility that the nerves are bruised and the signal is having a difficult time getting through. Do you have access to a Clinical Physiologist? This type of Physician might help in any additional diagnosis for your Daughter. They specialize in the function and movement of the body and work closely with Neurologists. Your Daughter should possibly be looked at by a Neurologist.
But if the vertebrectomy is lower and she says she is having problems with the upper part of her body, then i would say yes, she might need to be seen by a Psychologist as the procedure itself may have affected her. It is so difficult to say from here, and not being a medical practitioner, all I can offer is an opinion, but things take time.