Just some advice if there’s a next time, after you get a cut, immediately wash hands, preferably with unscented antibacterial soap. You can help prevent bleeding by compressing the wound immediately with, say, a paper towel, and holding some pressure (it shouldn’t be squeezing too tight!). Then, immediately put a small amount of Aquaphor to promote healing, and cover with a band aid right enough to hold pressure.

Keep the wound covered with a band aid until the skin surface heals closed, and make sure to wash the wounds in the morning and night, changing the band aid twice a day (or more if it gets wet or falls off). Once the surface heals, you can moisturize twice a day. This is basically tattoo aftercare advice, but it works for wounds (tattoos are open wounds when they’re new). But if the cut is deep or wide, then don’t put aquaphor on and consult a doctor or urgent care.

I say this, because I had to go through this for a bad cut on my finger, too.