The OP is factually incorrect.
Even prior to Donald Trump taking office, Hillary Clinton and the democrats were complaining about fake news because they believed that fake news stories (possibly done by Russians) contributed to her losing the 2016 election. They were even considering legislation to crack down on fake news.
The "fake news" train really picked up steam with Donald Trump and his supporters when CNN and Buzzfeed decided to report on the unverified Russia dossier (which isn't technically "fake" news, but it is incredibly bad journalism).
At any rate, I find it interesting that you specifically call out Fox News, but make no mention of MSNBC (Rachel Maddow and Trump's tax return, anybody?).
But yes, it is true that trust in the media is at a record low...and I don't think that's a bad thing. The media generally doesn't deserve our trust.
It may be a bit much to call the media "fake news," but it is true that Fox News, MSNBC, CNN, etc. (all of which we may generally classify as "the corporate media") are all heavily biased. Even if we ignore political biases, they are all biased towards sensationalism (because that's what gets eyeballs), towards corporate interests (because they are all owned by massive corporations) and towards the establishment.
Did you see the interview where a CNN executive basically admitted that the Russia scandal is basically groundless, but they insist on covering it anyway because CNN is a business and the Russia scandal gets them views?
And do I really need to mention how the corporate media has a track record of manufacturing consent (to use Noam Chomsky's phase) for war/foreign military interventions? Do I need to mention the role that CNN played in manufacturing consent for the war in Iraq?
"Weapons of mass destruction"? What would you call that but "fake news"? But CNN covered it.