Periodic Fever, Aphthous Stomatitis, Pharyngitis, and Adenitis (PFAPA) Syndrome: This diagnosis is considered due to the patient's recurrent episodes of sore throat, fatigue, and maculopapular rash, which are characteristic of PFAPA syndrome. The episodic nature of her symptoms, with periods of remission lasting up to 3 months, also supports this diagnosis.

Systemic Lupus Erythematosus (SLE): Despite previous blood work reportedly ruling out autoimmune disease, including lupus, the patient's symptoms of recurrent skin lesions, sore throat, fatigue, and hair thinning could still be suggestive of SLE, especially given the presence of a maculopapular rash on her cheeks and nose. Further evaluation may be necessary to confirm or rule out this diagnosis.
Adult-Onset Still's Disease: This condition is characterized by recurrent episodes of fever, rash, and joint pain, which could align with the patient's symptoms. The presence of a maculopapular rash and episodic nature of her symptoms make this a plausible diagnosis.
Ehlers-Danlos Syndrome: The patient's history of easy bruising (suggested by the initial presentation of dark purple sores around the breasts) and potential joint hypermobility (not explicitly mentioned but could be related to the fatigue and sore throat) might suggest Ehlers-Danlos Syndrome, although this would not fully explain all her symptoms.

Malignancy (e.g., Lymphoma): Although less likely, it is crucial not to miss a potential malignancy, such as lymphoma, which could present with recurrent episodes of fever, fatigue, and rash. The patient's symptoms of sore throat and fatigue, which improve with rest, could be indicative of an underlying malignancy.
Infectious Diseases (e.g., Endocarditis, Osteomyelitis): Recurrent infections or a chronic infectious process could explain some of the patient's symptoms. It is essential to consider and rule out such conditions due to their potential severity and need for specific treatment.
Vasculitis (e.g., Granulomatosis with Polyangiitis): Vasculitis could present with a wide range of symptoms, including skin lesions, fatigue, and recurrent infections. Missing this diagnosis could lead to significant morbidity and mortality.

Sjögren's Syndrome: This autoimmune disorder could explain some of the patient's symptoms, such as fatigue and potentially the skin lesions, although it is less likely given the absence of prominent dry eye or dry mouth symptoms.
Relapsing Polychondritis: Characterized by recurrent episodes of cartilage inflammation, this condition could potentially explain some of the patient's symptoms, especially if there are any respiratory or auditory manifestations not mentioned in the history.
Autoinflammatory Disorders (e.g., TNF Receptor-Associated Periodic Syndrome): These are rare genetic disorders that lead to recurrent episodes of inflammation and could potentially explain the patient's symptoms, although they are less common and would require specific testing for diagnosis.