I can see a little redness, doesn't look serious but I can only guess as to the cause. It may be that the dragon has bitten on something hard so now if the owner is sort of force feeding her it can aggravate the sore. If they can get to another more qualified vet that might shed some light on the problem. Three weeks on antibiotics can be really harmful to a dragon though and can take the appetite away . I'd not use any more antibiotics for a while for sure. See if the owner can get some other soft body insects like silkworms or hornworms that are loved by most dragons.
BTW, how old is she ?