TheLethalCarrot's answer is the simplest explanation. Though if one wanted to find some way to interpret the full prophecy from the books so as to make the show's depictions to date a fulfillment thereof...
We should keep in mind that prophecies are free, if not required, to be vague and figurative.
"And when your tears have drowned you..."
This is certainly speaking figuratively, as if she was literally drowned by her own tears there would be no need for anyone to be choking any life out of her. We can think of it as meaning
When your grief and loss overwhelm and warp you [into an even more vicious and stubborn person]
Now to the second part,
"...the valonqar shall wrap his hands about your pale white throat..."
If we're already being figurative, and we're dealing with a prophecy, why should we be literal here? It does not have to involve literal hands, it does not have to involve her literal throat, nor does it have to be her literally choking (or being choked).
Let's take the valonqar to be Tyrion, instead. He is Daenaerys' Hand. After Dany herself, he is the highest ranking person in her faction and commands the siege on King's Landing. He even tells Jaimie that he knows the city's defenses and weaknesses inside and out, and that the city will fall. So we can read this part as meaning
Tyrion, Hand of the Queen, will lay siege to your city and keep...
So that the last part
"...and choke the life from you."
leaving you no escape but death.
And there you have it, prophecy fulfilled as depicted.