I'd substitute the word "normal" with "common". Normal is a very hard thing to define, but a general form of anxiety is extremely common worldwide. You're absolutely not alone in feeling this way.
If the anxiety is 'raw', and it seems to affect how you feel about pretty much anything, it's considered generalised anxiety. In regards to generalised anxiety, it's very normal to feel this way under a variety of circumstances. Generalised Anxiety has a heap of causes ranging from stress, diet, environmental factor, genetics, etc.
If you feel that the generalised anxiety may be becoming excessive or way too frequent without a cause, the first thing I'd examine is everything you consume, overall physical fitness, etc. For one example, regular or high caffeine intake is a surefire way for some people with specific genetics and physiology (but certainly not all people) to develop some pretty significant underlying anxiety. Everyone is different, and you can get anxiety from even the smallest things such as certain chemical compounds in food or environment. Usually it's an indicator that the body is trying to tell you it's unhappy in someway, but it's purely a reactive response, and sadly our body is very poor at telling you -what- has made you feel this way. I've found it's helped me immensely to ask these questions when I notice anxiety kicking in:
What have I eaten / drunk / consumed in the last 12 hours?
What kinds of physical activities have I undertaken, or not undertaken?
Have I encountered, or been in contact with negative people who are toxic or miserable (This is a big one! Humans are social creatures, and as such we're very dependent on social interactions as a need, just as we need water and oxygen. Toxic or bitter people can be infectiously negative. You might not realise it until later, but if you find that you walk away from a conversation with someone feeling worse than when you entered, it's a sign that person is bad business.)
If you can find a good diet that works for you, and build a friendbase of good, supportive friends, you'll notice your problems with anxiety get -a lot- better, I guarantee it. :)
At the same time, keep your chin up! The world has good and bad to offer, and things are always capable of getting better for you if you're willing to give it a serious shot. You got this!