Butka, I am in your team)))
To eliminate this annoying frustration I started dedicating a lot of time to my... writing. Yes, At first sight It sounds odd. But spending much time on writing (I mean writing a long meaningful texts , that causes maximum of my concentration on sentence-building ) helped me to construct my sentences in foreign language faster. Moreover , after such a practice finding appropriate words during a CONVERSATION became easier. Sometimes it is useful to write without help of Internet because all necessary vocabulary we already have and what we need is just to find a proper word in our heads.
Oh, sure. I am highly articulate when I talk to myself. It's only when I talk to people that I struggle finding synonyms, ending up repeating the same basic words over and over.
I think that's because when I talk to others I assume they won't wait for my finding the best words and double checking if they are the right ones. And it is so despite that I honestly don't care that much for avoiding mistakes. It's the pressure to talk fast that makes me use the words that pop up first. And these are usually just a few most commonly used (by me) phrases.
I believe practice is the solution here. Each conversation brings new words, even if just a few, that you used, so if you go on using them, they will become your "go to" words when you speak next time.
Once again, you are not the only one dealing with that problem. I think it's something normal. I'm used to having the same problem, but I would say that its intensity has decreased a lot. How? Wel, because I have included in my study routine the habit of reading different types of readings, then I can learn more words and refresh others that I don't use as often. It has worked for me, maybe it can work for you as well.
P.S. Read aloud, it also will help you to improve your pronunciation.
I am currently experiencing the exact same thing in Portuguese.
My advice would be : breathe and no pressure (no nail biting).
Plus I am sure your teacher is patient so no worry... :)
Do you have what's app or telegram for learning English?