Fog and edge computing are very popular for enabling low-latency processing in applications that require quick responses, such as autonomous systems, smart cities, and the Internet of Things (IoT). While these technologies support effective real-time data processing, managing budgets and meeting strict deadlines remain major challenges. Traditional load-balancing algorithms focus more on workload distribution and performance but often overlook cost optimization and deadline requirements. In this study, we introduce the Budget-Aware Load Balancing Algorithm with Strict Deadline Constraints (BALBA-SD), which aims to use resources efficiently while respecting tight deadlines in fog and edge computing. BALBA-SD uses a hybrid approach to dynamically assign tasks between nodes based on the budget and project deadlines. Simulation results show that BALBA-SD is highly effective at meeting deadlines compared to other methods and can reduce execution costs by 21.79% relative to traditional approaches. This makes BALBA-SD a strong choice for deadline- and budget-focused load balancing in fog and edge computing.