Wow, most people only speak one language and they do that badly. You speak 3! Your English is good in that post.
If this anxiety is affacting your day to day life you might want to consider a short corse of therapy. You could probably use a book or website.
"Mind Over Mood" is a respected book. http://www.amazon.com/Mind-Over-Mood-Change-Changing/dp/0898...
MoodGym is a respected Australian website. https://moodgym.anu.edu.au/welcome
If you decide to use a therapist make sure you find someone with a reputable registration and that you are clear going in what you want to work on. Cognitive Behaviour Therapy is probably useful. It should take 8 to 14 weeks at an hour per week.
> And I tend to make a lot of syntax errors. I also tend to rely on documentation a lot. Furthermore, I tend to make a lot of stupid mistakes when I'm speaking English even though I have been living and attending college in an English-speaking country for the past three years.
You are not stupid, and the mistakes you make are not stupid. English is hard! There are at least 7 different ways to pronounce "ough" (like in "rough" or "through" etc). It's tough for people to learn. Stresses on syllables come in different places. You might think that making mistakes is always bad and that everyone will judge you. Some people will judge you, but many more won't notice and even of the people who notice there'll be some people who don't care.
You can use techniques like cognitive behaviour therapy to help ease the intrusive thinking.
The Australian website "Mood Gym" is a good quality site that provides computer guided CBT: https://moodgym.anu.edu.au/welcome
Or there are books. I've heard "Mind over Mood" is good.
http://www.amazon.co.uk/Mind-Over-Mood-Change-Changing/dp/08...
http://www.amazon.com/Mind-Over-Mood-Change-Changing/dp/0898...
Or you can go see a therapist. For stuff like this you should specify a very short course - 3 sessions of an hour each - before you start, and make sure that the therapist is focussed on this specific problem.
CBT aims to help you learn your moods and the thoughts that cause them; then to think about your thoughts and the evidence you have for them; and then to think if there is other evidence, and does this new evidence reduce the intensity of the emotion. It's an iterative process.
http://www.amazon.com/Mind-Over-Mood-Change-Changing/dp/0898... I'm sure if you look you could find other books that are a little more academic than instructional, if that's what you're after.
Edit to add: Even though it looks like it might be, this isn't soft touchy-feely self-help bullshit. CBT has been proven as an effective treatment for things like depression. There's real science here.
(http://www.amazon.co.uk/Mind-Over-Mood-Change-Changing/dp/08...)
(http://www.amazon.co.uk/Overcoming-Anxiety-Helen-Kennerley/d...)
Find a friend to help give you a poke now and again.
Here's an Australian website that is often recommended.
(http://moodgym.anu.edu.au/welcome)
A few weeks work will drastically reduce anxiety.
{Start-up idea: MoodGym but better.)
