Yesterday I tripped over and since then I have pains above my elbow (I don't know how is that bone called). It's not swollen and it hurts mostly when I want to lift something or for example open a door or even take a book or phone or anything. It also hurts when I move like when I'm putting my coat on. The pain is not too severe but I'm wondering if the bone could be broken.
It is possible that you may have sustained a nondisplaced fracture of the humerus. These are sometimes called a hairline fracture. It would not be a displaced fracture of the humerus, as these are unstable, and you would not be able to use the upper extremity.
But, the only way to know for sure, would be to have the elbow and humerus x-rayed.
So, again, the bone could be cracked. Usually, these are treated with a few days of rest and protection, followed by gradual increase in activity. But, if you want to know for sure, you will need to see your physician.