Make sure to keep it clean using an antiseptic and then put the Antibiotic on the wound, and do this every day until the wound/scratch is completely gone. If you notice any blackness develop around the area of the wound, then post another photo of it, as that is the first indication that you have a problem.
FYI ABOUT CATS AND DRAGONS: AHBD said it very directly, "Keep the cat away from the Dragon from now on", which you must do. I'm not as nice or as friendly as him (lol, no big secret there
), and I will honestly tell you that cats are one of the most common causes of early Bearded Dragon deaths. Honestly, your Dragon's tank should be kept only in a room that is TOTALLY off limits to the cat and the door must always be latched. If you scroll through the Beardie ER you'll see post after post after post of cats lifting the lids off of the Dragon's tank, getting the Dragon out of the tank and torturing them for hours, knocking the entire tank over and then getting a hold of the Dragon, and just cats who were allowed by their owners to sit near the Dragon, with the owner totally supervising them both, when suddenly the cat quickly bites down on the Dragon's skull, and that's it.
****The other thing that most Beardie owners don't know is that ALL CATS contain an enzyme in their saliva that is fatal to Reptiles, so if your cat bites your Dragon, even if it's not a bad bite, if the bite breaks the skin and their saliva gets into the wound, the Dragon can die. Also, since cats are constantly licking their paws, if your cat has just licked his paws and then he scratches your Dragon and the saliva gets into the open wound, this can also kill your Dragon if the wound is not cleaned-out soon enough. So this makes keeping your Dragon totally isolated from your cat all the more crucial.