Ehrlichiosis: This diagnosis is the most likely due to the combination of symptoms such as arthralgia, myalgia, elevated liver function tests (LFTs), and thrombocytopenia, which are commonly seen in ehrlichiosis. Ehrlichiosis is a tick-borne bacterial infection caused by Ehrlichia species, and it often presents with these specific clinical findings.

Anaplasmosis: Similar to ehrlichiosis, anaplasmosis is a tick-borne disease caused by Anaplasma phagocytophilum. It can present with fever, headache, arthralgia, myalgia, elevated LFTs, and thrombocytopenia, making it a plausible diagnosis given the symptoms.
Southern Tick-Associated Rash Illness (STARI): Although STARI is more commonly associated with a rash, it can also present with systemic symptoms such as fever, headache, and myalgia. However, elevated LFTs and thrombocytopenia are less commonly reported, making it slightly less likely but still a consideration.
Babesiosis: This tick-borne illness, caused by Babesia parasites, can lead to symptoms like fever, myalgia, and thrombocytopenia. Elevated LFTs can also occur, especially in more severe cases. The absence of a specific mention of hemolytic anemia, which is a hallmark of babesiosis, does not rule it out entirely.

Rocky Mountain Spotted Fever (RMSF): Although RMSF typically presents with a characteristic rash, fever, and headache, it can be fatal if not treated promptly. The presence of thrombocytopenia and elevated LFTs could be seen in RMSF, especially in severe cases. Given its potential for high mortality, it is crucial not to miss this diagnosis.
Tick-Borne Relapsing Fever (TBRF): TBRF, caused by various Borrelia species, can present with recurring episodes of fever, headache, and myalgia. While less commonly associated with elevated LFTs and thrombocytopenia, its potential severity and the importance of early treatment make it a "do not miss" diagnosis.

Powassan Virus Disease: This rare tick-borne viral illness can cause symptoms ranging from mild fever and headache to severe neuroinvasive disease. While it might not typically present with the combination of arthralgia, myalgia, elevated LFTs, and thrombocytopenia, its potential for severe outcomes warrants consideration in the differential diagnosis, especially in endemic areas.
Tick-Borne Encephalitis (TBE): TBE is a viral infection that can cause a range of symptoms from mild to severe, including neurological manifestations. It is less commonly associated with the specific combination of symptoms mentioned but should be considered, particularly in travelers to or residents of endemic areas in Europe and Asia.