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.
We cannot tell you why you are worrying: the best person to understand the why is you. But we can tell you that there is no need to worry. Reading a paper is one of the everyday tasks of research, and while it is an important part of the job, you will have plenty of time to learn the ropes. If you're a beginner, just read through the paper, takes notes of the main points you understand, and the points you don't understand that seem important. You can then research those, or ask to your advisor or colleagues.
In the end, reading papers is a statistics game: there are very few papers that are so crucial to your own research that you positively have to understand every single last idea and word in them (I would say, less than 10 during a PhD). Most of the time, some ideas are usefuls, some are not, plus there is a lot of redundancy between papers… I used to be quite scared that I would have missed some important paper in the bibliographic search, but quite frankly it's rare for an important idea to exist in a single place and never have been reüsed or quoted.