Although those can very well be physical symptoms of anxiety, and sometimes anxiety symptoms differ from person to person, you might want to also get checked by a doctor to rule out any other potential health concerns.
Stress, can reak havoc on the body. You should try to relax and put your mind at ease so that you do not develop any issues with high blood pressure, or heart palpitations, etc.
Stress is also an indicator that something in your life needs to be changed. It's like an internal alarm clock, poking at you every night, making you wake up at 4 am. It's a survival technique, something in your psyche is telling you something in your life needs to be dealt with or changed.
What is it that is keeping you awake at 4 am? Is it work related? Is it family related? Is it school related? I think a common stresser is work related for many people. If your job is causing you stress to the point of waking you up filled with anxiety at 4 am, you might want to re-consider your job. Because putting your job before your health almost always causes your health to get worse.

My dad had a stressful job for many years, he didn't get along with his management and this caused him a great deal of stress, until one day he had a heart attack at his desk at work. He survived, but he went on disability soon thereafter.

So make sure you're listening to what your body is telling you. And this doesn't necessarily mean you would need to quit your job, for example. It could just mean that you need to find better ways of managing your stress while at work so that it doesn't wake you up in the early mornings. I'm just using work as an example here, so ask yourself what is really waking you up.