In recent years, Internet of things (IoT)-enabled health monitoring wearable devices have become a trend in healthcare systems, regularly collecting vital sign data from patients and uploading them to the cloud. Through on-demand search queries, data are shared with third-party healthcare service providers (HSPs) to monitor patients' health status and provide timely diagnoses. To ensure privacy and security, patient health data should be encrypted before being uploaded to the cloud. The cloud can give search encryption services. However, current searchable encryption technologies still have problems with forward privacy security and verifiability. This paper proposes an IoT-cloud-enabled healthcare data system incorporating a searchable encryption method with forward privacy and verifiability. By designing a trapdoor permutation function, we render the resulting output indistinguishable from meaningless random data to the adversary. Thus, the adversary cannot judge the relationship between a newly inserted record and a past search token, and therefore, the system realizes forward privacy or forward secrecy. We propose a multi-keyword search verification mechanism based on a pseudo-random function (PRF). Our approach solves verifying the correctness of search results in the top-k search scenario with partial search results. A formal security analysis proves that our scheme achieves forward privacy preservation, which can help guarantee healthcare data privacy. Additionally, a performance evaluation shows that our method is efficient and effective, providing an information security system to preserve patient privacy in IoT-enabled healthcare systems.