You had me in stitches, David. (Sorry...)
Don't feel too silly for sustaining your injury. A few years ago, I was in the process of moving house and packing boxes. I picked up a box that contained my blender to have a good look at it - the bottom fell out, as did the blender. The blade sliced through the top of one foot, which split open like a book.
I immediately burst into tears - not from the pain, because luckily the blade was so sharp and clean it barely hurt - but because I was terrified I would bleed on the carpet of the rental property, and have to pay for a new one. I managed to avoid painting the carpet in my own blood and got myself to a public hospital, where I got stitched up for free by a (very-overqualified!) MD.
Your urgent care experience does sound pretty painful. I think your partner was sensible to have a snack before you set off, when knows how long you could have been waiting...