Systemic Lupus Erythematosus (SLE): The patient's positive ANA screen with a titer of 1:160 and a homogeneous pattern, along with a secondary titer of 1:320 and a speckled pattern, strongly suggests an autoimmune process. The presence of chronic constant nausea and new-onset OCD-like symptoms could be manifestations of neuropsychiatric SLE. The elevated platelet count and normal to slightly elevated WBC count also support this diagnosis.

Juvenile Rheumatoid Arthritis (JRA): Although the patient's symptoms do not directly point to joint inflammation, JRA can sometimes present with systemic symptoms such as nausea and can have a positive ANA. The absence of specific joint symptoms does not rule out this diagnosis entirely.
Chronic Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can present with chronic nausea and may have extraintestinal manifestations, including psychiatric symptoms. The elevated platelet count could indicate an inflammatory process.
Thyroiditis: Given the slightly low T4 and normal TSH, thyroiditis could be considered, especially if there are symptoms suggestive of thyroid dysfunction. However, the primary symptoms do not strongly suggest this diagnosis.

Neuroblastoma: Although rare, neuroblastoma can present with a wide range of symptoms, including nausea and behavioral changes. The elevated platelet count could be seen in cases of neuroblastoma due to paraneoplastic syndromes.
Lymphoma: Certain types of lymphoma can present with systemic symptoms such as nausea and may have psychiatric manifestations. The slightly elevated WBC count and lymphocyte percentage warrant consideration of lymphoma.
Infectious Diseases (e.g., Lyme disease, Tuberculosis): These can sometimes present with nonspecific symptoms, including nausea and psychiatric symptoms. A thorough exposure history is necessary to consider these diagnoses.

PANS (Pediatric Acute-onset Neuropsychiatric Syndrome): This condition is characterized by the sudden onset of OCD symptoms and can be associated with various infectious triggers. However, the chronic nature of the nausea and the positive ANA make this less likely.
Mitochondrial Disorders: Certain mitochondrial disorders can present with a combination of gastrointestinal and neuropsychiatric symptoms. However, these are rare and would typically be associated with other systemic symptoms or a family history of similar conditions.
Autoimmune Encephalitis: This is a rare condition that can present with psychiatric symptoms and may have associated systemic symptoms like nausea. The presence of a positive ANA could support an autoimmune etiology, but specific antibodies for encephalitis would need to be tested.