"Mouth Rot" is a general infection that spreads throughout the mouth, killing all of the tissue along it's way, and it occurs VERY OFTEN in Bearded Dragons, not just Iguanas, so that's incorrect information. However, we can't really tell if this is an infection such as Mouth Rot, as we can't see the inside of her mouth...
That being said, your Dragon looks extremely sick, probably suffering from a severe Calcium Deficiency and MBD, and if there is blood in her urates she could have a high count/load of parasites, or she could be impacted...Did she have a normal bowel movement along with the urates?
My guess here is that this Dragon was not under an adequate
UVB light or fed an adequate diet, and is suffering greatly from MBD, she has a bit of bony deformity in her jaw/face that is typical with MBD, and the lack of appetite, lethargy, etc. is also indicative of MBD, though it could also be other issues on top of the MBD too, like parasites, infections, etc.
What kind of set-up do you have her in? What
UVB light do you have? And her temperature zones?
She is going to need an extremely strong UVB tube and fixture, a long T5 strength UVB tube is highly recommended, along with a bright-white colored Basking Bulb right alongside the T5 UVB tube, both over the Hot Side of the tank, with her Basking Spot/Platform directly underneath both lights. Both lights need to be on for at least 13-14 hours every day. That's step #1.
She's most likely severely dehydrated, but don't stress her out by
bathing her a lot, they do not absorb any
hydration by soaking in water, that's a myth, they have to get all of their
hydration through their mouths just like we do. So you need to start dripping water on her snout for her to lick off, give her as much as she'll lick off, several times a day. You're probably going to have to also syringe feed her a nutrition replacement slurry/paste, such as Oxbow Critical Care, which you can order online. In the meantime you can try to syringe feed her some Squash Baby Food that has a pinch of Calcium Powder and a pinch of a Reptile Multivitamin in it, see if she'll lick that off.
She can't handle any medications right now, like antibiotics or antiparasitics, they will surely kill her (renal failure), so you need to get her
hydrated and get some nutrition in her first, and get her under a strong T5 UVB tube and Basking Bulb at proper temperature zones.