How would I know if I've been brainwashed? Thinking about the "re-education" camps in parts of the world. They attempt to replace one idiology in you head with another and is considered brainwashing.

On the other hand, the first idiology got in their head by their parents. So is that not also brainwashing of a sort?

How would I know if I have been brainwashed to believe things that aren't necessarily true? How can I prevent being brainwashed by the media?

For example I believe that we can find out how the world works through science and experiment but maybe I've just been brainwashed to believe that and really the only way to find out about how the world works is by divine revelations by angels.

So how can I tell?
I'll go about this question focusing on the definitions, rather than jumping onto the answer proper. Clarifying definitions may already help you a step closer to an answer.  


  
  On the other hand, the first id[e]ology [of children] got in their head by their parents. So is that not also brainwashing of a sort?
  


the definition of Brainwashing...:


  a forcible indoctrination to induce someone to give up basic
  political, social, or religious beliefs and attitudes and to accept
  contrasting regimented ideas


...readily answers this Q, namely a kid's brain is a clean slate, virtually devoid of "political, social, or religious beliefs". So no, this is not brainwashing.


  
  How would I know if I have been brainwashed...[?]
  


Brainwashing was coined by journalist Edward Hunter in September 1950 described how Mao Zedong’s Red Army used terrifying ancient hypnotic techniques to turn the Chinese people into mindless, Communist automatons. "Brainwashing” was a word-for-word translation from xi-nao, the Mandarin words for wash (xi) and brain (nao). In the Korean war later in the '50s, thousands of American soldiers, including high-ranked officers, petitioned to end the war, made false claims of war atrocities by the Us and even refused to re-enter the army after they were freed. The US jumped on it and said these people were brainwashed. However, when the media hype was over, scientific research revealed what truly made these soldiers following the ideas of the "communists"; they were tortured (source: Smithsonian Magazine). 

Your question seems also to radiate the mystical origins of the word brainwashing, namely that the media can somehow hypnotize you and change your thoughts mysteriously. Those are false believes. Of course the media affects your thinking, but it cannot "brainwash" you.


  
  I believe that we can find out how the world works through science and experiment but maybe I've just been brainwashed to believe that and really the only way to find out about how the world works is by divine revelations by angels.
  


Some people believe God created the earth and all its life on it. Others choose evolution to be key to life, and the big bang for the creation of the universe instead. It's a choice you can make. Many scientists are also believers. In other words, you don't have to choose, and support both views. Nothing brainwashy about either side.