We present FairHealth, an open-source Python library that provides a unified, modular framework for trustworthy machine learning in healthcare applications, with particular focus on low-resource and low-income country (LMIC) settings such as Bangladesh. FairHealth addresses four critical gaps in existing healthcare AI toolkits: (1) the absence of integrated fairness auditing for biosignals and clinical tabular data; (2) the lack of privacy-preserving federated learning tools compatible with standard ML workflows; (3) missing explainability tools tailored for low-bandwidth clinical decision support; and (4) no existing toolkit covering Global South healthcare datasets. Built from five peer-reviewed research contributions, FairHealth provides six modules covering federated learning with homomorphic encryption (fairhealth.federated), intersectional fairness metrics (fairhealth.fairness), hybrid fuzzy-SHAP explainability (fairhealth.explain), multilingual dengue triage (fairhealth.lowresource), equitable disaster aid allocation (fairhealth.equity), and public dataset loaders (fairhealth.datasets). All datasets used are publicly available without institutional data use agreements. FairHealth is installable via pip install fairhealth(PyPI: pypi.org/project/fairhealth/) and available at https://github.com/Farjana-Yesmin/fairhealth.