Any doctor who sees you in Singapore is required to take notes detailing the reason and nature of your visit. So yes, there will be a record that you had a prescription for a Plan B pill in Singapore, at least at the clinic you visited.
There is a soon to be introduced National Electronic Medical Record system (NEHR) that will mean that your doctor will input all these details into a centralised online record. This was previously only optional (meaning the doctor and clinic could choose not to input patient data into this system), but will soon become compulsory.
The idea behind the NEHR is to enable any doctor treating patients to have relevant medical information that could help in treatment and diagnosis. It will also prevent data from being lost should a doctor retire.
Till date, all public sector medical institutions are using the NEHR to input patient information. However, many private clinics (as of June 2018) are still not inputting information into the NEHR.
If you want to reduce the chances of your information going into the NEHR, you can go to a private GP clinic that looks like it's been around a long time - chances are, they have not yet adopted the NEHR system.
To answer the second part of your question, all your medical records (be it on the NEHR or not) are kept strictly confidential. Employers and insurers will also be prohibited from accessing your medical history in the National Electronic Health Records (NEHR).
If you prefer not to have any of your medical data in the NEHR, you have 1 of 2 options:
1. You can have your data included but not made available to any doctor accessing the database. If you change your mind later, your medical history can be uploaded.
2. Alternatively, you can choose not to have any of your medical data in the system. In this case, no historical data will be available.
