Encouraging people who may be infected with HIV to draw blood is a waste of public health resources and is likely to pose a threat to public health and safety.
It is recommended to go to the VCT (voluntary counseling and testing room) of the local CDC for free testing, which is completely confidential. The hospital's uncertain samples also need to be sent to the CDC for confirmation.
Where to go for testing has nothing to do with how long you are at high risk. The CDC in Nanjing has very standardized testing procedures and strong testing ability. Why not use such a good resource?