Deep pain is an unsophisticated but reliable test to evaluate how much injury there is to the spinal cord. Having deep pain is a good thing - there is still some functionality in the spinal cord. The fact that she is still able to control urination and BMs also indicates that there is some connection going through the spinal cord.
Don't get too concerned about the yelp, she's also getting used to being handled in new ways. It is important to avoid torque to the spine to prevent further disk injury.
I've used Adequan with some success but it's not a cure, just a valuable anti-inflammatory tool.
The way the hydrotherapy works is to support weight while allowing mobility and limb movement, perhaps re-learning how to walk. The heat from the water could also be of some benefit.