Nowadays, there are many fragmented records of patient's health data in different locations like hospitals, clinics, and organizations all around the world. With the arrival of the COVID-19 pandemic, several governments and institutions struggled to have satisfactory, fast, and accurate decision-making in a wide, dispersed, and global environment. In the current literature, we found that the most common related challenges include delay (network latency), software scalability, health data privacy, and global patient identification. We propose to design, implement and evaluate a healthcare software architecture focused on a global vaccination strategy, considering healthcare privacy issues, latency mitigation, support of scalability, and the use of a global identification. We have designed and implemented a prototype of a healthcare software called Fog-Care, evaluating performance metrics like latency, throughput and send rate of a hypothetical scenario where a global integrated vaccination campaign is adopted in wide dispensed locations (Brazil, USA, and United Kingdom), with an approach based on blockchain, unique identity, and fog computing technologies. The evaluation results demonstrate that the minimum latency spends less than 1 second to run, and the average of this metric grows in a linear progression, showing that a decentralized infrastructure integrating blockchain, global unique identification, and fog computing are feasible to make a scalable solution for a global vaccination campaign within other hospitals, clinics, and research institutions around the world and its data-sharing issues of privacy, and identification.