The patient's symptoms and findings suggest a likely diagnosis of HIV with disseminated histoplasmosis. Let's break down the rationale behind this diagnosis:
- **Persistent cough and weight loss:** Common symptoms associated with disseminated infections, especially in immunocompromised individuals such as those with HIV.
- **Skin lesions described as umbilicated papules and nodules:** These can be associated with several conditions, but in the context of an HIV-positive patient, they are characteristic of fungal infections like histoplasmosis.
- **Chest x-ray findings of multiple bilateral nodular infiltrates:** Nodular infiltrates in the lungs support the possibility of a disseminated infection.
- **Negative sputum CBNAAT for tuberculosis:** This reduces the likelihood of tuberculosis as a cause, especially given the presence of immunosuppression-induced lower CD4 count, where opportunistic infections are more common.
- **Low CD4 count:** Highlights the patient's vulnerability to opportunistic infections like histoplasmosis.
Considering the given options:
- HIV with disseminated histoplasmosis: Consistent with all the patient's symptoms and laboratory findings.
- HIV with disseminated cryptococcosis: Typically would involve central nervous system symptoms more prominently, and not as commonly associated with skin lesions described.
- HIV with molluscum contagiosum: While umbilicated papules might suggest this, the systemic symptoms and chest X-ray findings point away from this diagnosis.
- HIV with tuberculosis: Despite similar lung findings, a negative CBNAAT test makes it less likely, especially given the low CD4 count and skin manifestations.
The correct diagnosis based on the information provided is HIV with disseminated histoplasmosis.