The department that can carry out professional testing must be a laboratory or an AIDS screening laboratory. Generally, larger public hospitals can carry out AIDS screening and testing. You can go to the dermatology department, infectious diseases department or infectious diseases department of the hospital you mentioned to find a doctor to open an application form for AIDS testing and go directly to the laboratory for blood test. It would be better if there is a simple clinic, where you can keep accounts.
It is suggested to go directly to the local CDC for AIDS screening, which is convenient, confidential and free, much more convenient than the hospital.