When bleeding occurs under the nail plate because of an injury, it is referred to as a “traumatic hematoma.” As blood pools in the hematoma, it eventually creates enough pressure that the rate of blood flow is reduced to the point where normal clotting occurs, then further bleeding stops.
As long as the normal skin barriers around the nail are not violated, it would be very difficult if not impossible for an infection to occur. If the nail plate fractures or if the distal edge of the nail has separated away from the nail bed, then caution would be appropriate—cleansing with hydrogen peroxide and applying topical antibiotic ointment should be sufficient to prevent infection. It should not be necessary to remove the overlay.
If the client experiences pain due to the buildup of the hematoma, an old trick is to have her take a paper clip, unfold it, heat one end over a gas flame (be careful not to burn the fingers holding the paper clip) and carefully touch it on the nail plate over the hematoma. It should be possible to melt a small hole in the nail plate which then relieves the pressure. If this is done, hen care must be taken as outlined above to avoid infection. Eventually the hematoma will grow out and the nail should return to a normal appearance. One last word of caution: Occasionally, malignant melanomas can appear under fingernails and may look just like a hematoma. A “hematoma” that gradually enlarges may not be a hematoma at all and should be evaluated by a dermatologist. -- Dr. MacGougall
Let me start by answering the last part of your question first. Yes you should be worried about an infection starting under this nail. Whenever there is bleeding, no matter what part of the body, an opening through the outer protective barrier of the body has been created. It sounds as though the protective seal between the hyponichium and the nail plate was broken. This opening in medical terms is called a “portal of entry” and through it organisms, such as bacteria and fungi, can gain entry into the underlying tissues. Given the right condition an infection will ensue. So as a general rule, whenever one sees bleeding she must always think about the possibility of an infection occurring in the area.
If the nail is partially lifted off the nail bed as the result of the injury, I do not think that the gel overlay should be removed. The procedure of removing it would only add trauma to the already injured nail and nail bed. Instead, trim the nail back as short as possible to reduce the risk of further injury from catching it on things and causing further lifting from the nail bed. The client must keep the area clean and apply an antibiotic ointment under the free edge of the nail as protection against infection. At the first sign of an infection (extra pain, swelling, redness, heat, or drainage) the client should seek medical help. -- Dr. Mix