can a hospital discharge a person having a hard time breathing and have serious open wounds bed sores. and can her doctor prescribe medications

This is a question of standard of care.  If the discharge leads to harm, worsening of the conditions and permanent injury or need for invasive surgeries, then it may well violate the standard of care.   As to their decision, that would not be unlawful based upon these facts of discharging you.  As to the doctor, not enough information.