Explaining that you have been busy
I’ve been very busy!
Keeping myself busy.
Been keeping myself busy.
I’m swamped. Swamped=overwhelmed, as with a swamped boat
I’m snowed under. Snowed under=as if buried in snow.
I don’t have time to breathe.
I don’t have time to think.
There aren’t enough hours in the day.
Not a moment to spare.
I’ve been running around like a chicken with my head cut off. (informal slang)
I’ve been running around like a chicken with its head cut off.(informal)