Yep. Been there. Done that. I cut deeply about 6-8 weeks ago when my wife was out of town. I can look at a cut and say, "that needs stitches." I looked at my cut, had that thought, and knew I'd ruin my wife's visit with our daughter and new granddaughter if I told her I got stitches.
Bled like crazy, but cleaned it up, slathered with antibiotic gel, and wrapped it firmly with a water-proof bandaid. Repeated when changing the bandaid every 24 hours. Now I have to look hard to find the scar.
That was a lesson I learned when flying for the Navy in my young, "live like you're invincible" days. Almost chopped the end of a finger off when pruning a bush. Finger stitches would mean being grounded for a couple weeks or more. Not happening. Can't even see that scar anymore.
Heal fast, Dan. And buy some waterproof bandaids.