I would translate your sentence as 我现在非常渴了。 This is because I read "I am now X" to mean that you are are emphasizing that X is a new situation. You create the same emphasis in Chinese by putting the 了 at the end.
I'm trying to find the rule of when to start with the time/adverb and when to start with the pronoun. English isn't picky. My sense of Chinese is that it isn't as picky as Duo presents but I could be wrong about that.