People frequently exposed to health information on social media tend to overestimate their symptoms during online self-diagnosis due to availability bias. This may lead to incorrect self-medication and place additional burdens on healthcare providers to correct patients' misconceptions. In this work, we conducted two mixed-method studies to identify design goals for mitigating availability bias in online self-diagnosis. We investigated factors that distort self-assessment of symptoms after exposure to social media. We found that availability bias is pronounced when social media content resonated with individuals, making them disregard their own evidences. To address this, we developed and evaluated three chatbot-based symptom checkers designed to foster evidence-based self-reflection for bias mitigation given their potential to encourage thoughtful responses. Results showed that chatbot-based symptom checkers with cognitive intervention strategies mitigated the impact of availability bias in online self-diagnosis.