On-road emergencies necessitates the availability of the patient's medical records to the emergency centers for better treatment. However, these medical records are often encrypted to preserve the patient's privacy. Revealing the secret key used to encrypt these records to the emergency center would not only give unlimited unauthorized future access to the medical records but also pose privacy concerns for the patient. In this paper, we propose a secure medical records access scheme that can be used to serve the patient effectively. An emergency medical center is able to decrypt a patient's medical records without revealing the secret key used to encrypt them with the help of the patient's smart phone and the cloud server. We use proxy re-encryption scheme to trigger a re-encryption process at the cloud server by sending the required credentials. With the help of the cloud server, only a specific emergency center is able to decrypt the medical records and access the patient's medical history. Our scheme allows in-time and more efficient health care and recovery in extreme life-threatening situations. Our analysis and evaluations show that the proposed scheme can secure the medical records and preserve the privacy of the patient with acceptable computation and communication overhead.