Why am I worrying when I read a paper? I'm beginner in research and I'm doing my PhD. I would like to know why when I read a paper I worry as if I have exam tomorrow and I have to prepare for it. How can I ignore that feeling and increase my productivity?
Perhaps one little "therapy" often relevant is to try to remind yourself that you are the authority in reading papers critically, and the goals are about progress, not evaluation of you by some third party.

It is understandable that "school" has left one with an excessively paranoid concern about being attacked, being "checked-on", being examined, being doubted, and so on. Indeed, "school" often includes exaggerated measures that express very clearly an antagonistic, adversarial attitude of "teachers" toward "students". Naturally, many negligent students are able to ignore this pressure, while students who were already doing the right thing are the ones who feel that somehow they're not doing enough. A similar dynamic exists in many human enterprises.

So, again, the thing to repeat to yourself over and over is that now you are to function as an authority, you are to assess these papers. The point is not so much any more someone else's assessment of your "performance" (often on meaningless, contrived, artificial tasks).

In particular, the common "teaching-examining" devices of "trick questions" should be forgotten. When encountering a new idea, don't immediately be worrying how someone could use the idea to trip you up, but, instead, what constructive use you could make of it. In particular, if it does not (at least for the moment) seem useful to you, then don't spend a lot of time on it just for the sake of self-defense against trick questions! Nevertheless, one should often keep a "pointer" to seemingly useless ideas, because their utility may be discovered only later.

But don't study things whose utility seems null. Move on, just keeping a "bookmark", so if/when something percolates into your head later, you can go back and look a second time.