Lyme Arthritis: This is the most likely diagnosis given the history of a tick bite and subsequent joint swelling. Lyme disease, caused by the bacterium Borrelia burgdorferi, is known to cause arthritis, particularly in children, and the presentation matches the classic symptoms of Lyme arthritis.

Septic Arthritis: Although less likely than Lyme arthritis given the context, septic arthritis is a consideration in any child presenting with acute joint swelling, especially if the joint is hot, red, and painful. Bacterial infections can cause septic arthritis, and prompt diagnosis and treatment are crucial.
Viral Arthritis: Various viral infections can cause arthritis in children. While the tick bite points more towards Lyme disease, viral causes should be considered, especially if the Lyme test is negative.
Reactive Arthritis: This condition occurs as a reaction to an infection elsewhere in the body, not directly due to the infection itself. It's less likely but should be considered if other infections are identified.

Rheumatic Fever: Although less common in areas with good access to healthcare, rheumatic fever can occur after a streptococcal infection and affects the heart, joints, and other tissues. Given the patient's cardiac history, missing this diagnosis could have significant implications.
Endocarditis: In a child with a pre-existing cardiac condition, endocarditis (infection of the heart valves) is a critical diagnosis not to miss. While the presentation doesn't directly suggest endocarditis, the combination of a cardiac history and potential for bacteremia (e.g., from a tick-borne illness) makes it a concern.
Osteomyelitis or Bone Infection: Infections of the bone can present with joint swelling and pain. These conditions require prompt antibiotic treatment to prevent long-term damage.

Southern Tick-Associated Rash Illness (STARI): Caused by the lone star tick, this condition presents with a rash similar to erythema migrans (the rash associated with Lyme disease) but is less likely to cause joint symptoms.
Rocky Mountain Spotted Fever (RMSF): Although RMSF can cause joint pain, it's more commonly associated with a characteristic rash and severe systemic symptoms. It's a tick-borne illness but less likely to present primarily with joint swelling.
Other Tick-Borne Illnesses (e.g., Anaplasmosis, Ehrlichiosis): These illnesses can cause systemic symptoms including fever, headache, and sometimes joint pain, but they are less commonly associated with isolated joint swelling.