I'm exhausted, I've just done a long journey.
'Esausto' — e-ZAU-sto. The 'au' is a diphthong — say it as one smooth sound.
Use after returning from a long journey, work trip, or holiday. Travel fatigue is universally understood and accepted as a reason to need rest before seeing anyone.
'Sono esausto/a' means 'I am exhausted'. 'Ho appena fatto un lungo viaggio' means 'I've just done a long journey'. The passato prossimo with 'appena' emphasises the recency — you just got back and haven't recovered yet.
Sono appena tornato/a, ho bisogno di recuperare.
I've just got back, I need to recover.
'Recuperare' (to recover/get back on one's feet) — very natural
Il viaggio mi ha distrutto/a.
The journey destroyed me.
Dramatic but very Italian — expressive and generates sympathy
Devo smaltire il jet lag.
I need to get over the jet lag.
Used after international flights — immediately understood even in Italian
Even a journey of a few hours by train or car is considered tiring in Italy. Unlike in some cultures where long commutes are normalised, Italians view travel as genuinely draining and expect you to rest afterwards.