Patients with schizophrenia often present with cognitive impairments that may hinder their ability to learn about their condition. These individuals could benefit greatly from education platforms that leverage the adaptability of Large Language Models (LLMs) such as GPT-4. While LLMs have the potential to make topical mental health information more accessible and engaging, their black-box nature raises concerns about ethics and safety. Prompting offers a way to produce semi-scripted chatbots with responses anchored in instructions and validated information, but prompt-engineered chatbots may drift from their intended identity as the conversation progresses. We propose a Critical Analysis Filter for achieving better control over chatbot behavior. In this system, a team of prompted LLM agents are prompt-engineered to critically analyze and refine the chatbot's response and deliver real-time feedback to the chatbot. To test this approach, we develop an informational schizophrenia chatbot and converse with it (with the filter deactivated) until it oversteps its scope. Once drift has been observed, AI-agents are used to automatically generate sample conversations in which the chatbot is being enticed to talk about out-of-bounds topics. We manually assign to each response a compliance score that quantifies the chatbot's compliance to its instructions; specifically the rules about accurately conveying sources and being transparent about limitations. Activating the Critical Analysis Filter resulted in an acceptable compliance score (>=2) in 67.0% of responses, compared to only 8.7% when the filter was deactivated. These results suggest that a self-reflection layer could enable LLMs to be used effectively and safely in mental health platforms, maintaining adaptability while reliably limiting their scope to appropriate use cases.