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Your finger will likely swell no matter how hard you hit it. This is the most common response to such trauma. If the hit wasn't too forceful, your finger may just swell for a couple of days. If the only symptom you see is swelling, place an ice pack on your finger to help relieve the swelling and pain.  You can take over-the-counter pain medication to help relieve the pain as well. An NSAID (nonsteroidal anti-inflammatory drug) such as ibuprofen (Advil, Motrin IB) or naproxen sodium (Aleve) can help relieve the inflammation and pain. Take as directed on the packaging.  You don't need to see a doctor unless the swelling won't go down, you develop serious pain or numbness, or you can't move your finger all the way in or all the way out. If the swelling is really bad and you are in extreme pain, you may have fractured your finger, especially if you hit your finger quite hard. If your finger looks contorted and is extremely sensitive to the touch, you likely fractured your finger. This may be accompanied by bleeding skin or a smashed fingernail. If you think you have a fracture, seek medical attention. You need an X-ray and the doctor may give you a finger splint or some other form of treatment. Do not put a splint on your finger unless a doctor tell you to do so. If your finger is bleeding after you hit it, you need to clean the wound so you can assess the damage. If there is visible bleeding, cleanse the wound with running warm water. Run the warm water over the wound with the run-off going down the drain, not back into the wound. Then, using a gauze pad, cleanse the entire wound surface with Betadine or other cleansing solutions.  Put pressure on your wound for a few minutes to slow the flow of blood, which will help you assess how deep the wound is and if you need to see a doctor. If there is excessive bleeding or squirting blood, seek medical attention immediately. Once you've cleaned the wound, you need to evaluate the finger for any lacerations, or cuts. The wound still may bleed a little while you check, which is fine. Lacerations often show up in the form of tears or flaps of skin on the surface of your finger. Any obviously destroyed tissue or any skin that has been torn off and left a raw bleeding finger pad needs to be examined by a doctor. Lacerations may need to be stitched if the wound is 1/2 inch or larger. However, if there is a section of completely destroyed skin, it is unlikely to be salvaged.  Many doctors will still suture damaged or destroyed skin over the raw finger pad as protection while new skin grows back over the area. The skin will them be removed once new skin has formed. Lacerations may be shallow and stop bleeding soon after you get them, especially if you didn't hit your finger that hard. If this is the case, wash the wound, put antibiotic ointment on them, and wrap them with a bandage. Since your hand and fingers are an intricate system of muscles, tendons, and nerves, it's important to examine your finger for signs of tendon injury. Tendons connect muscles to your bones. Your hand has two types of tendons: flexor tendons, on the palm side, that bend the fingers; and extensor tendons, on the back of the hand, that straighten the fingers. Cuts and smashes can damage or even sever these tendons.  A torn or cut tendon in the finger will make it impossible to bend your finger. A cut on the palm side of the hand or near the skin folds at the joints of your fingers may signal injury to the tendon below. You may also feel numbness due to associated nerve damage. Tenderness on the palm side of your hand may signal an injured tendon. You may want to request a hand surgeon if you show any of these signs, as repairing the hand and fingers can be a very intricate process. If you hit your fingernail with the hammer, there may be significant damage to it. Look at your fingernail and assess the damage. If there is a small blood blister underneath the fingernail, there is no need to see a doctor. Just ice the wound and take over the counter medication if there is any initial pain. If the pain lasts for days, if the blood blister takes up more the 25% of your fingernail, or if the blood is causing significant pressure under your fingernail, seek medical attention. You likely have a subungual hematoma.  You may also find that a portion of the fingernail has become detached or has been cut. If you have a significant cut in the nail bed, seek medical attention because you will likely need stitches. If you don't get it treated, the cut may prevent nail growth, cause the nail to grow in a distorted manner, or cause infection. If the fingernail is partially or entirely gone, seek medical attention right away. This is a serious problem and needs attention. The fingernail may be removed or stitched up until a new, healthy fingernail can grow back. This can take up to six months.

Summary:
Check for swelling. Respond to a fracture. Clean the wound. Assess the lacerations. Look for tendon injury. Evaluate the fingernail.