Are there any immediate concerns Cut index finger on top at the knuckle?

With any injury the first thing that you should evaluate is the ABC's, airway, breathing, and circulation. With a cut finger airway and breathing are most likely not of much concern unless the finger got cut in addition to another injury such as a fall. Here the immediate concern is the "c" part of the equation, circulation. This means that your biggest concern is blood loss. The first thing you want to evaluate in terms of circulation is to quickly determine what kind of vascular injury is present. If it is an arterial injury the blood will be a bright red and will bleed in "spurts" that correlate with the heart beat. This is the most serious injury to expect in this case because one can loose a lot of blood quickly if untreated. If the injury is to a vein (most likely in this case) then the blood will be a darker red and will ooze out slowly. An injury to a lesser vessel such as capillaries is of less significance. The cut should be cleaned under cold water, dried, and bandaged. Ideally, you should use an antibiotic cream (such as neosporin) applied to the bandage to minimize infection. Until the bandage can be applied try to keep your hand above your heart to reduce blood loss and make bandaging easier. Ice may also be applied. Multiple layers of bandaging may be needed. If the bleeding seems severe or doesn't stop after twenty minutes then you should consider going to an emergency room or urgent care clinic. Long term, you should be concerned with infection. Although you may have used neosporin, you may still get an infection from bacteria on your skin such as staph or strep, or from the source of the cut (i.e., tetanus from a piece of metal found in the dirt that cut your finger). Infection can be suspected if the tissue around the cut becomes tender, turns red or purple, and/or you come down with a fever within days after sustaining the cut. In this case you need to get professional treatment.