Health providers need to share patient information across healthcare networks efficiently and securely to improve medical and health services. Timely data synchronization among relevant parties is crucial for effectively containing and preventing the worsening of the condition. However, ensuring rapid information sharing while maintaining the security of sensitive patient data remains a pressing concern. In this paper, we introduce a cloud storage integrity auditing scheme that can protect auditors from procrastinating and preserve the privacy of sensitive information. Our proposed system requires healthcare institutions to encrypt sensitive patient data before uploading it to the cloud. It mandates the use of a data sanitizer for the secure processing of encrypted data blocks. Auditors must verify data integrity and promptly submit their audit results to the blockchain within a predefined time frame. Leveraging the time-sensitive nature of blockchain technology, healthcare institutions can monitor auditor compliance within the allotted validation timeframe. We conducted comprehensive security analysis and performance evaluations to demonstrate the feasibility and effectiveness of our solution in addressing the challenges of secure and timely cloud storage in healthcare settings.