Is the questioner’s act of swearing that she would not take blood pressure medication—even though her blood pressure was high at the time of the examination and the doctor recorded a lower value based on her oath—considered a false testimony, and consequently, is her salary unlawful? And what should she do?

The salary from permissible work is lawful (halal (definition)), and there is no sin upon you for answering the doctor negatively about your high blood pressure, because your answer was truthful. It is possible that the condition developed later. There is no blame upon you for remaining in the job if the illness does not prevent you from performing it.