Sorry, there is no hospital that meets your requirements. There is Tongren Hospital in the southeast north gate of the nearby big hospital, but there is no direct access. Take the Qing' an line to the southeast west gate and take another bus for a few stops. You should check it yourself. Tongren Hospital has a good attitude and advanced hardware facilities, because it is a private hospital. If it is 20 yuan. It takes 30 minutes to go there by bike.
There is also the People's Hospital of Confucius Temple. Take 105, and take a short walk. It's closer than Confucius Temple, about 50 minutes one way. It will take at least 2 hours to go back and forth with disinfection.