What is an idiom for being engaged in something? [closed]

I am looking for an idiom to express someone is completely engaged in or busy with an activity.

For example,

When all my peers were busy preparing for the upcoming exam, I had to assist my mother in the shop.

Is there an idiomatic expression that expresses the "busy doing something . . ." part to emphasize the peers were solely busy with their exam preparations and could not think of doing anything else?

While I was knee-deep in research, working to improve my answer, everyone else was out celebrating the new year.

From Merriam Webster, knee-deep:

b: deeply engaged or occupied
knee-deep in work

A tangible metaphor for how involved one can get in the work, to be "knee-deep" in something means the depth your involvement is significant enough that you can't be pulled away too easily. You're not necessarily "in over your head" yet (Lexico), but it's keeping you quite occupied, and you're too busy to be pulled away just now.

For your example, "My peers were knee-deep in exam preparation with no time to help out in the shop."

I would have answered your question earlier but I was so wrapped up in my New Year breakfast.

wrapped up in: idiom

Definition of wrapped up in:

fully involved or interested in (something) ”I was (completely) wrapped up in my work, so I didn't hear you.”

Merriam Webster

Be immersed in something is an idiomatic expression that may convey the meaning you are looking for:

if you are immersed in something, you spend most of your time doing it or thinking about it as in:

• David was deeply immersed in student politics.

(Macmillan Dictionary )