What is the ruling on swimming in mixed-gender pools for the treatment of back pain, given the unavailability of male-only pools, and should this sport be abandoned despite the severity of the illness?

Swimming in mixed pools is not permissible. It is also not permissible for men to enter their designated pools except with a loincloth or something that covers the 'awrah, due to the saying of the Prophet, peace and blessings be upon him: "The lands of the Ajam (non-Arabs) will be opened for you, and you will find in them houses called حمامات (bathhouses). So, men should not enter them except with loincloths, and prevent women from entering them except if she is sick or in post-natal bleeding." If only such pools are available, one must seek times when they are empty, or look for an alternative for sport or treatment.