Keeping myself busy.
Been keeping myself busy.
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 tо think.
There aren’t enough hours in the day.
Not a moment to spare.
I’ve been running around with my head cut off (informal)
I’ve been running around like a chicken with its head cut off(informal)
Explaining that you have been busy (объяснение, что заняты)