нет -- "по уши в чём-то" это чисто русский сленг, англоязычные такое не говорят

hiiii

Hi Anya, There are three versions of the idiom according to McGraw Hill's Dictionary of American Idioms and Phrasal Verbs: *up to one's neck (in something) and *up to one's ears (in something); *up to one's eyeballs (in something) having a lot of something; Fig. very much involved in something; immersed in something. (*Typically: be ~; get ~.) I can't come to the meeting. I'm up to my neck in these reports. Mary is up to her ears in her work. I am up to my eyeballs in things to do! I can't do any more! Hope that solves the problem here

To the person who said eye balls instead of ears Lol yeah eyeballs are further up your head so it is more work. It sounds natural. Both of them are good idioms to say that I have way too much work. Don’t use this - but it means the same thing, busier than a one armed paper hanger with crabs....ok if somebody had read that and is ROFL, then I met my objective- brightened someone’s day.

In my area in the US, that doesn't sound like a natural thing to say. Up to my ears doesn't sound like an idiom that exists.