Lyme Disease: Given the patient's recent hiking activity in a wooded area, the presence of a rash (possibly erythema migrans), fatigue, headaches, and mild chills, Lyme disease is a highly plausible diagnosis. The rash's location on the back and its size (20 cm) are consistent with the characteristic presentation of Lyme disease.

Southern Tick-Associated Rash Illness (STARI): This condition, caused by the bite of the lone star tick, presents with a similar rash to Lyme disease but is typically found in the southern United States. Symptoms can include fatigue and headache, making it a consideration.
Rocky Mountain Spotted Fever (RMSF): Although the rash in RMSF usually appears later in the course of the disease and is more generalized, the initial presentation can sometimes mimic other conditions. The patient's exposure to ticks in a wooded area and symptoms like headache and fever make RMSF a possible diagnosis.
Ehrlichiosis/Anaplasmosis: These tick-borne illnesses can present with fever, headache, fatigue, and sometimes a rash, although the rash is less common. Given the patient's recent tick exposure, these should be considered.

Rabies: Although extremely rare and not typically presenting with a rash, any bite or scratch from an animal in a wooded area necessitates consideration of rabies due to its almost invariably fatal outcome if not promptly treated.
Tick-Borne Relapsing Fever (TBRF): This condition, caused by various Borrelia species transmitted by soft ticks, can present with recurring episodes of fever, headache, and muscle pains. A rash may or may not be present. Given the potential for severe outcomes if untreated, it's crucial not to miss this diagnosis.

Babesiosis: A parasitic disease transmitted by ticks, babesiosis can cause fever, fatigue, and sometimes a rash, but it's more commonly associated with hemolytic anemia. It's rare but should be considered in patients with significant exposure to ticks.
Tularemia: Caused by Francisella tularensis, tularemia can be transmitted by the bite of an infected tick. It presents in different forms, one of which (ulceroglandular tularemia) includes a skin ulcer at the site of the tick bite, along with systemic symptoms like fever and headache. Although rare, its potential severity warrants consideration.