Sounds to me that the nurse tore the vein as they “dug a bit.” Probably a newbie nurse.
You don’t say which extremity the wound is. I’m assuming it is the arm. You don;t say how much you are bleeding, so I’m assuming because you’re still conscious, and A/O enough to write competently that it is not too bad, just annoying.
If you find it too worrisome or annoying, apply a pressure bandage and don’t take any blood thinners like aspirin or St. John’s Wort for a few days. If you are taking prescription blood thinners, you shouldn’t have given blood in the first place and you need to call the doctor who prescribed them before you stop taking them.
A pressure bandage is simple to make. For a wound this size, take a couple of gauze 4×4s and fold them twice so they become very thick 2×2s. Wipe the area with another 2×2 soaked with whatever antiseptic you have around:: leftover Betadine from a past injury, rubbing alcohol, hydrogen peroxide, or hard liquor. Apply the folded 4×4s directly to the wound. Wrap the wound around your arm a few times tautly with a 4in or 10cm wide strip of gauze, but not so tight that the distal part of your arm becomes discolored or loses feeling or pulse. Then fasten the wrap with tape or tie it so that the tension is maintained. Change with a new bandage if you have the material. Examine the bandage for fresh red blood are any discolored exudant. Examine the wound for radiating redness, increased swelling, discolored exudant. That’s the Cadillac version.
Most people, unless they are accident prone, don’t have 4×4s or rolls of gauze laying around the house in sterile packaging unless they are accident prone or have children. So, substitute the folded 4×4s and gauze strip with non-synthetic, absorbent, clean rags. Soak the clean fabric that you are substituting for the folded 4×4s with a ~half inch (1cm+) of waded up fabric in your available antiseptic and apply. Rip a strip of fabric 4 inches wide and long enough to wrap around your arm at least 4 times. It doesn’t have to be sterile, but it should be clean. Wrap it tautly around your arm 3 times as described above, then rip it down the middle and give the ends two twists so they won’t rip further under tension. Then bring the ends around to the side of of the pressure pack and tie it off with a square knot. Ta-da! Homemade pressure bandage.
These are good for puncture wounds of all sizes and are often used in field-expediencies including gun shot and shrapnel wounds to the extremities and even the chest. They often stop the bleeding entirely or slow bleeding enough to buy precious time until the patient can get to a doctor and a place equipped to deal with the injury. Knowing how to properly apply a pressure bandage is a good thing. .
In your case, the bleeding should stop in the next 24 hours. If after 48 hours your bandage still shows frank, red blood, or signs of infection, you should go to a clinic.
Man, I got my hands on some good coffee here.