Speaking of brain activity and responses, a friend shared this video with me - how stress affects your brain:
This video gives a nice overview of many important brain systems and what they do, while talking about the effect of stress. The video also talks briefly about the epigenetics, the ways in which the environment can trigger certain genes to express. This means that, even if you have a genetic predisposition to stress and anxiety, a nurturing environment can keep that gene from expressing.
An important extension of this concept is the biopsychosocial model, which states that biology, psychology, and social environment combine to determine health across one's lifespan.
Experience can change the brain, though your brain becomes less plastic (changeable) as you age. This is why a small child may recover from a head injury that would be fatal to an adult. The brain is able to rewire itself, especially prior to the age of 6. And while the brain changes discussed in the video are real, they represent a worst-case scenario of stress response. If you experience normal amounts of stress or only occasional instances of high stress, you'll probably be fine. But if you experience high chronic stress, you'll want to do something to cope with that - whether it be talk therapy, lifestyle changes to minimize stress, and/or medications for anxiety.