you definitely need new boots.
duct tape can give a temporary fix for footwear. but it doesnt last long.

In the old days, the Indians and the pioneers were experts at making new shoes on the go. The Indians actually carried spare pieces of leather (skin) for moccasins, and deer sinew to tie them together. That was how important it was to make new footwear quickly.

You did well to remember the duct tape.