As the OP has verified in the comments, the injury is in fact called an abrasion.
Abrasion is a wound caused by rubbing or scraping the skin or a mucous membrane; a “skinned knee” and a “floor burn” are common examples. To treat the injury, the wound should be washed, a mild antiseptic or antibiotic ointment applied, and the wound covered with sterile gauze.
Basically, the following happens when one injures oneself causing an abrasion:
- The top layer of the skin (Epidermis) gets torn off by the friction, revealing the dermis and its minor blood vessels below. This is why the wound is hardly bleeding.
- Nerv ends in the dermis are also revealed, this is why the comparably small injury causes a lot of pain.
- The open wound secrets exudate, mainly consisting of blood serum.
The layers of the skin:
Image Credit: Wikipedia.org
Usually, abrasions do not lead to infections. Nevertheless, it can't hurt to be cautious.
Because the wound doesn't bleed a lot, dirt does not get washed away naturally that easily and it is recommended to rinse the wound first. In Germany, it is not recommended to rinse the wound with water (albeit the water having very good quality, it is not sterile) and instead, it is sufficient to mechanically clean the wound with sterile compressions.
This has the advantage over disinfectants that the blood clotting is not inhibited. Opinion on this differs in the U.S., where normal cleaning is still recommended.
However, it hardly matters for a minor injury like this. If you do not have a sterile compression at hand, I recommend to use water instead.
Afterwards, the open wound should be covered with a liquid bandage or a sterile bandage.
Visit a doctor if signs of a severe infection should appear or if the abrasion covers a large area. The wound will then require special treatment.