Due to a pituitary issue when I was younger I have maybe a bizarre world record of the smallest feet and hands on a fully grown man. My feet and hands are normal looking but very small. They were tiny as a baby and just never grew that big. Thought you all would find it interesting - I know it makes for good chat at parties!
Even worse. I wear size 12 and a half. Surprise! They don’t make half sizes after 12… So, either swimming in a 13, or super snug in a 12.
I feel your pain! A couple of sneaker makers have 12.5.
Get good thick insoles maybe? Extra padding and will help make a 13 fit better