It is common to hear people say things like "I am drowning in work" or "He is drowning in debt". It refers to being incapable of overcoming your work or problems. It is also common to hear someone say that they 'Just can't keep their head above water'

“You don't need water to feel like you're drowning, do you?” ― Jodi Picoult, Nineteen Minutes He does mean drowning. It is a quote. I am not sure if he wants this translated into Turkish, if he asking us to interpret it or if he is just stating it as an inspirational quote of some sort.

It can be a simile for feelings.

I think that you mean drawing not "drowing"...