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I suspect you got your information on care from a pet store. Most people do. While we should be able to rely on such information, unfortunately, it is often wrong. They sell people the wrong lighting, advise the wrong foods, and often don't know the correct temperatures for the various reptiles. After months of things not being quite right, the animal becomes ill. Much of what you have been told is wrong, and I suspect that is why Sandy is having so much trouble. Even though you have been trying so hard to keep her healthy, when you didn't have correct information to begin with, things are going wrong. When a beardie becomes frantic as Sandy has, it means she is in distress. Shedding for a month is also a sign of something not being right.
I’ll start with a first aid measure.Buy some Pedialyte (yes, the kind for human infants). Prepare a shallow bath consisting of 1/2 water and 1/2 Pedialyte. Soak Sandy for about 20 to 30 minutes twice a day. Reptiles can absorb the electrolytes and fluids through their vents (where droppings pass out), so make the water deep enough to cover the vent. Be sure to supervise closely. The soak will help with dehydration and may loosen the shedding skin so it can come off.
Next, we need to make some changes.
The biggest problem is that Sandy is freezing cold. A beardie who is cold will be lethargic, not want to eat a lot, and may even try to hide. I'm surprised that at these temperatures, she will even eat when handfed. The very coldest part of the cage should be 85*F to 90*F. For a youngster this age, the basking spot should be at least 105*F to 110*F. The latest research on bearded dragons has shown that they can't even begin to digest their food properly until their internal body temperature reaches 98*F. Being cold-blooded, the only way for that to happen is for them to lie in a very hot basking area.You can increase the temperature by using a higher wattage bulb in the basking light fixture, lowering the fixture itself (but not so low that she can be burned on it), or by adding a second fixture. If you need a second fixture, you don't have to buy something expensive from a pet store.If you live in an area that has farm stores, you can buy a clip-on metal light fixture made to keep baby chicks warm for just a few dollars. Don't buy the accompanying bulb, however. You need an ordinary incandescent bulb in the basking light. Hardware and home improvement stores sell similar light fixtures as work lights.
The sand substrate may be why Sandy is having shedding problems. Pet stores often recommend it because it is a money maker, but it does frequently lead to serious health problems, including impaction. It’s also a leading cause of eye infections, respiratory irritations, and skin problems. Here is a reputable site where you can read more:
I'll post this much now, and will be back with more in a few minutes.