He’s worn the glove on that left hand when there was an issue, but then told the press the hand was completely healed but he continued to wear the glove out of superstition (coincided with his longest streak of not throwing a pick).
I do remember one game where it looked like he reaggravated it, but then said afterwards it was his funny bone and he was trying to weather a burning sensation. Don’t know if the left is still broken, but we do know Josh doesn’t cry over injuries or embellish them for sympathy like certain other QBs.