Lyme Disease: This is the most likely diagnosis given the history of a tick bite and a rash that has been present for 3 weeks. Lyme disease, caused by the bacterium Borrelia burgdorferi, is commonly transmitted by tick bites and often presents with a characteristic rash (erythema migrans) at the site of the bite, which can appear within a few days to a month after the bite.

Southern Tick-Associated Rash Illness (STARI): This condition, also known as Masters disease, presents with a rash similar to erythema migrans but is caused by a different bacterium. It's a consideration in areas where the Lone Star tick is common.
Rocky Mountain Spotted Fever (RMSF): Although RMSF typically presents with fever, headache, and a petechial rash, it can occasionally manifest with a maculopapular rash. Given the tick bite history, RMSF is a plausible diagnosis, especially in endemic areas.
Ehrlichiosis/Anaplasmosis: These are tick-borne bacterial infections that can cause fever, headache, and sometimes a rash. While not as commonly associated with a distinct rash as Lyme disease, they are important considerations in the differential diagnosis of tick-borne illnesses.

Rickettsial Diseases (e.g., RMSF, Typhus): These diseases can be severe and life-threatening if not treated promptly. A high index of suspicion is necessary, especially in patients with severe symptoms or those who have been in areas where these diseases are endemic.
Babesiosis: A parasitic disease transmitted by ticks, babesiosis can cause severe hemolytic anemia, especially in individuals without a spleen or with compromised immune systems. It's crucial to consider this diagnosis in patients with unexplained anemia or hemolysis after a tick bite.

Tularemia: Caused by Francisella tularensis, tularemia can be transmitted by tick bites and presents with a variety of symptoms, including skin ulcers, fever, and lymphadenopathy. It's a rare but potentially serious disease.
Tick-Borne Relapsing Fever (TBRF): This disease, caused by several species of Borrelia, is characterized by recurring episodes of fever and is transmitted by soft ticks. It's relatively rare and more commonly associated with exposure to infected ticks in rustic cabins or caves.
Powassan Virus Disease: A rare but potentially severe tick-borne viral disease that can cause encephalitis or meningitis. It's an important consideration in areas where the virus is known to be endemic.