First of, don't keep the humidity up. Dragons are somewhat sensitive to high humidity, making them prone to respiratory infections. Just keep his temps up (105-110).
The chlorhexadine Is an antiseptic, similar to betadine. It can also be used to soak the area.
For lack of a picture, I'll ask some questions and rattle off some things to look for.
Discoloration is not always tail rot. Grey, faded looking or dull discoloration is part of shedding. This can be patchy to start out and can take a week or so progress. Tail rot is a darker sometimes black color. Usually it starts at the tip of the tail due to injuries or stuck sheds.
Is the discoloration recent or has it always been like that?
Is/was the dragon housed on sand or other dusty substrate? Colored sands are notorious for staining scales.
Is the tail still flexible and responsive? It is delicate at the tip, but it should not feel dry or brittle.
Does the area have a waxy or thick feeling or the scales seam to have a different texture than the normal color area? Retained sheds can discolor, and can lead to complications if not treated.
Has she shed her tail with you, if so did it all come off?
Has the dragon been injured on the tail? Bites, cuts, pinches and such.
If the color is not recent, and the tail doesn't feel strange or Injured, it could be part of her pattern. If the color is grey/dull/faded looking, it is likely shed. If there is potential it is a retained shed you can soak her daily until it loosens.
Keep an eye on it and make sure it sheds clean on the next cycle.
If the tail is dry and brittle, or worse yet breaks off you should see a vet, if possible. The same is for if the discoloration is associated with a bite or injury. The tissue has been damaged and there is potential for infection to develop. Chlorhexadine is one of the treatments, but there is potential need for the use of antibiotics. If you choose not to see a vet, continue the chlorhexadine and monitor for if the discoloration moves up the body. If it does, you should see a vet the infection has begun spreading. It might be helpful to take daily photographs to keep tract.