Question

وقت سر خاراندن ندارم

Answer 1

I'm tied up!

I'm far too busy.

I'm completely snowed under.

I'm up to my ears/neck in work!

I have tons of work to do.

Answer 2

+1 for Mr.Ali Karimian.Also I suggest : 

I am fully busy / engageg.

Answer 3

Pardon my French, but there's a very informal equivalent too:

I'm too busy to pee

It is used as an acronym too:

IM2BZ2P

http://goo.gl/ePQI8R

Answer 4

I.m as busy as a bee

hectic

Answer 5

Rushed off my feet

 I have a lot on my plate.

 I'm chasing my tail or running (a)round in circles,

 I'm running (a)round like headless chickens.

 I have my nose to the grindstone or that I have my head down.

 I need to try to have a good work-life balance, so I don't bust a gut (work too hard)!