There are quite a few different idioms for being busy in English. You might be up to your eyes, eyeballs, elbows or neck, snowed under, drowning, swamped or knee-deep in/with work. You can also be rushed or run off your feet. You could even say that you’re up to your nose in grindstones – one I came up with the other day.
You can also be up to your ears in work in Russian (po ushi), and up to your neck in Hebrew (עד הצוואר).
In Scots there’s an expression, up tae ma oxters in stour, which means ‘up to my armpits in muck’ and can be used to mean that you’re very busy.
In Spanish you can be flooded with work (estoy inundado/a), or be up to your neck, ears, nostrils or even balls with it (estoy hasta el cuello / las orejas / las narices / las huevos de trabajo)!
In Danish you can say that work is hanging far out from your throat (Det hænger mig langt ud af halsen), and you can say the same in German (das hängt mir zum Hals ‘raus). In German you can also be stuck in work up to the neck (bis zum Hals in Arbeit stecken), up to the chin (bis zum Kinn), or sink/drown in work (in Arbeit versinken).
In Swedish you can be overwhelmed or oversnowed with work (Jag är överhopad / översnöad med arbete).
In Czech an excess of work is said to come up over your head (mám toho až nad hlavu).
In Japanese you can be too busy for words (isogashiittaranai), or you can be so busy that you would even accept help from a cat’s paws (neko no te mo karitai).
In Arabic-speaking countries you might be sinking in work, not have time to scratch your head, or by busy to the last fuzzy hazy limit of your head hair (mashghool leshooshtoh).
Tamil speakers say that they don’t even enough time to breathe (mūccu vidaradku kūda nēram illai).