I am sorry for you. Hope you got another save.
No need to sell the badges. If you play the Demon City correctly (and fullfill at least one Status Check) you can make enough currency to get everything except Murphy's Hand (too expensive, even with savescumming during the auction). And if you only get the Emblem and Flo, it's still a big win.
Joker Badge allows you to fight Gargoyles + 1000 Gold, and Knight's Badge is important to farm Blood Ore/Crytals to upgrade your Swords. The Knight Badge also opens the treasure room to Bread. Show the badge to the boot-driving ghost. The Prince badge is the most useless and rather save to give away, It only allows to skip the Boss fight.