As Artificial Intelligence (AI) increasingly integrates into our daily lives, fairness has emerged as a critical concern, particularly in medical AI, where datasets often reflect inherent biases due to social factors like the underrepresentation of marginalized communities and socioeconomic barriers to data collection. Traditional approaches to mitigating these biases have focused on data augmentation and the development of fairness-aware training algorithms. However, this paper argues that the architecture of neural networks, a core component of Machine Learning (ML), plays a crucial role in ensuring fairness. We demonstrate that addressing fairness effectively requires a holistic approach that simultaneously considers data, algorithms, and architecture. Utilizing Automated ML (AutoML) technology, specifically Neural Architecture Search (NAS), we introduce a novel framework, BiaslessNAS, designed to achieve fair outcomes in analyzing skin lesion datasets. BiaslessNAS incorporates fairness considerations at every stage of the NAS process, leading to the identification of neural networks that are not only more accurate but also significantly fairer. Our experiments show that BiaslessNAS achieves a 2.55% increase in accuracy and a 65.50% improvement in fairness compared to traditional NAS methods, underscoring the importance of integrating fairness into neural network architecture for better outcomes in medical AI applications.