Immune Thrombocytopenic Purpura (ITP): This condition is characterized by low platelet count (thrombocytopenia) due to immune system dysfunction, leading to increased destruction of platelets. The recent viral illness could have triggered the immune system to produce antibodies against the patient's own platelets. The presentation of punctuate bleeding of gingiva, diffuse petechiae, and purpura over the torso and lower extremities, along with a platelet count of 90,000, strongly supports this diagnosis.

Infectious Mononucleosis: Given the recent history of viral illness with fever, chills, rhinorrhea, and lethargy, infectious mononucleosis (caused by Epstein-Barr virus) could be a consideration. This condition can sometimes present with a rash and thrombocytopenia.
Viral Hemorrhagic Fever: Although less common, certain viral hemorrhagic fevers could present with similar symptoms, including a rash, fever, and thrombocytopenia. However, the lack of severe systemic symptoms and the specific pattern of the rash make this less likely.

Meningococcemia: This is a life-threatening condition caused by Neisseria meningitidis, which can present with a petechial or purpuric rash, fever, and shock. Although the patient's current presentation does not fully align with meningococcemia, the potential for rapid progression and high mortality rate makes it crucial not to miss this diagnosis.
Thrombotic Thrombocytopenic Purpura (TTP): TTP is a rare disorder of the blood-coagulation system, causing extensive microscopic thrombi to form in the smallest blood vessels throughout the body. These thrombi consume platelets, leading to thrombocytopenia, and can cause a variety of symptoms including rash, fever, and neurological symptoms. It is essential to consider TTP due to its severe prognosis if left untreated.

Henoch-Schönlein Purpura (HSP): This is a form of vasculitis that affects blood vessels and is characterized by the deposition of immune complexes containing IgA antibodies. It can present with purpura, abdominal pain, arthritis, and renal involvement. While it's more common in children, it can occur in adults and should be considered in the differential diagnosis of a patient with purpura.
Disseminated Intravascular Coagulation (DIC): DIC is a condition characterized by both widespread clotting and bleeding in the vascular system. This results from the simultaneous activation of both the coagulation and fibrinolytic systems, leading to the formation of blood clots in small blood vessels throughout the body. The consumption of clotting factors and platelets can lead to bleeding complications. The presentation can be varied and includes thrombocytopenia, which makes it a rare but possible diagnosis in this scenario.