No, we don't.
Not without some serious editing first.
I voted to close this originally because in my opinion the OP will need to clarify whether they are looking for a cure for their nervousness (as the question now states), or whether they are looking to fix an interpersonal problem here.
The OP of this question struggles with speaking with English-speaking clients.
True. 'I'm far from self-confident, especially when visitors are "big" people.'. We can't cure nervousness here though!
Nervousness interferes with how we deal with people, making it on-topic on IPS.SE.
Fine. Although I'm still not sure what this OP is looking for, a cure for nervousness or a way to do these 'dealings' without showing their nervousness.
The first requires an intrapersonal solution, and is basically what the question is asking right now: How to overcome nervousness.
And in the body:
It's so hard to be myself at work. I persuaded myself several times that my director and those visitors are just people and they will never bite me, but I can't help feeling anxious. How can I overcome my nervousness
The second is an interpersonal skill, the ability to act normally despite nervousness.
The way this question is written makes it clear that the OP is looking for a cure for the nervousness, not a way to handle these interactions without showing the nervousness, and that makes it focused on an intrapersonal solution and that makes it off-topic here.
But even if you don't agree with the original close reason:
If the OP is willing to pick one, there are a few questions that have to be answered and there's some fluff that needs to go.
Almost 1/3 of them are English speakers, which I seldom expected before.
Does this mean the OP wasn't told this when accepting the internship?
Similar things recurred several times. I knew my coworkers next door, who are all Chinese and advanced English users, especially my demanding director, all heard the way I talked, which made me frustrated and feel like a fool. This is my first formal internship and it's an opportunity for my future career. The more I try to do a great job, the more worried I become about my performance. My director occasionally praised me for translating gallery paperwork from and into English (which is what I take care of, too) and doing some other chores, and I value her positive impressions on me. Even I cannot do the greeting thing as well, I don't want to be thought poorly of, due to my spoken English. There's another intern who majors in English literature and had been an exchange student in the U.K, able to chat in English naturally. I'm not jealous or mean to compete, but feel the pressure from time to time.
The parts that are struck through don't add any further detail/ details necessary for answering and can go.
In fact, I'm not always as anxious. Being an introvert, normally I can socialize with people and do public speaking. I also have a few English-speaking friends, with whom I'm not-that-easily inclined to chat in anxiety. They know I'm still a learner between intermediate and advanced, thus they'll never mind my speaking speed, which may turn slow when idiomatic expressions suddenly escape me at certain topics. When I have trouble understanding their speech, I ask for clarification without hesitation. (But we don't meet up frequently, so there are not enough opportunities for me to speak English after work. Maybe it partially explains my anxiety.)
This can all go, and be replaced with 'I have no trouble with public speaking
or speaking English outside of work'.
There's also a question here:
Being an introvert, normally I can socialize with people and do public speaking.
Is this supposed to read 'despite being an introvert' or 'Being an extrovert'?
So basically, besides picking what problem the OP wants addressed, they should also answer some questions and we should edit out the unnecessary fluff.
