This paper focuses on the Continual Test-Time Adaptation (CTTA) task, aiming to enable an agent to continuously adapt to evolving target domains while retaining previously acquired domain knowledge for effective reuse when those domains reappear. Existing shared-parameter paradigms struggle to balance adaptation and forgetting, leading to decreased efficiency and stability. To address this, we propose a frequency-aware shared and self-adaptive expert framework, consisting of two key components: (i) a dual-branch expert architecture that extracts general features and dynamically models domain-specific representations, effectively reducing cross-domain interference and repetitive learning cost; and (ii) an online Frequency-aware Domain Discriminator (FDD), which leverages the robustness of low-frequency image signals for online domain shift detection, guiding dynamic allocation of expert resources for more stable and realistic adaptation. Additionally, we introduce a Continual Repeated Shifts (CRS) benchmark to simulate periodic domain changes for more realistic evaluation. Experimental results show that our method consistently outperforms existing approaches on both classification and segmentation CTTA tasks under standard and CRS settings, with ablations and visualizations confirming its effectiveness and robustness. Our code is available at https://github.com/ZJC25127/Domain-Self-Adaptive-CTTA.git.