LB, a Band-Aid should not cut off circulation, unless you’ve applied it too tight.
To try to get the bleeding to stop, apply pressure with a clean tissue. Keep the pressure constant, not looking underneath for about 5 minutes and keep the checks to every 5 minutes until you see the bleeding finally slow to a stop. If you are doing this for 20 minutes and do not see any lessening, then I would go to the emergency room. ALERT – DO NOT USE SUPER GLUE on your skin. You may need stitches if it is a deep gash, but if the skin across the top is missing, they may not have what to sew down. The area where there is a joint is notorious for difficulties closing as the constant movement of the area disrupts the clot and the bleeding renews itself. Definitely go to to an urgent care center if the bleeding is not manageable and coming to a stop. I know this is getting to you long after your post, so I hope things have resolved themselves without restoring to any hardware products.