Hey LG, maybe the school didn't provide the proper PPE (Personal protective Equipment) for using a scalpel? e.g. cut resistant gloves:
https://en.wikipedia.org/wiki/Cut-resistant_gloves and safety glasses and cut resistant sleeves.
https://www.magidglove.com/store/protective-clothing/protective-sleeves/
Although in your case, I think you would need full body armor. I hope it wasn't a case of your neighbor was say right anded and you were left handed?
I do hope your doing better. You had stitches, so healing should be easier. What i do for deep cuts is cut adhesive strips do that there is only 3-4 mm of material across the cut. Once the threat of infection is gone, you can promote healing by closing the wound and letting air in. My mom recently had skin surgery and I played doc per his instructions. Clean with Hydrogen peroxide and use petroleum jelly. I used my judgment as to what I did each day.
The worst thing was removing bloody bandages from my father's hair (stitched in the hospital).
My bad cuts were:
1) A pinky squish with a hammer scrapping transformers. Scar is still visible. No doctors. No stitches. (16-18 YO)
2) Chain saw kickback. (I was 16-18 YO) No docs. No stitches.
3) A drill press drill catching on a piece of sheet metal because it was unclamped, (20-30)
4) Using a file to make a custom lathe cutter. the file slipped. (20-30)
5) Falling down a flight of stairs. (maybe 10 YO)
6) removing an exhaust system in a car. (15-16 YO)
7) The nail in your hand that caused a blue streak to run up your arm. (6 years old)
Valuable lessons were learned. The last stupid thing was a couple of splinters in the bottom of my foot. I removed them with the help of a trusty fiber optic inspection camera. Having the tools (really sharp pointy tweezers) like these
**broken link removed** to remove splinters really helps.