How long have you had her? What substrate is she living in/on? I'm assuming then that she does not have one of those hammocks, because that's often a cause of a dislocated shoulder/elbow.
I'm assuming this is an injury and not MBD, only because it just appeared suddenly, correct? Usually MBD happens gradually, so if she was fine one minute and then the next her leg was like that and she isn't using it, then it's most likely an acute/sudden injury. Plus, she's so small/young that usually MBD has not had time to set in yet, though it's not unheard of.
EXACTLY what UVB tube do you have (Brand, strength, wattage)? It will be written right on the tube itself if you don't still have the box. It will say something like "Reptisun 10.0 T8 15 watt" for example.
YOU NEED TO GET RID OF THE RED BASKING BULB IMMEDIATELY!!! Dragons see in full color just like we do, and any colored bulbs confuse night and day, cause eye issues, and not only that, you are trying to replicate NATURAL SUNLIGHT over the Hot Side of his tank, and you do this by putting a BRIGHT-WHITE colored Basking Bulb right next to a long UVB tube, so that they are side-by-side and sharing the top of the Hot Side of the tank, so he gets both lights while basking. So you can ONLY ever use bright-white colored bulbs!!!
You need to either go to a pet shop and buy a specific Reptile Basking Bulb that is bright white in color and is the correct wattage to put the temperatures within the correct ranges (usually a 100 watt bright-white basking bulb over the Hot Side of the tank in a 40 Gallon tank is correct, maybe a 75 watt)...OR, you can simply go to Lowes, Home Depot, Tractor Supply, Walmart, etc. and buy a regular Halogen Indoor Flood Bulb, the kind you would use in your home, the PAR38 kind. That's what most of us use, they are no different than the Reptile Specialty Basking Bulbs and they are a lot cheaper usually. If you choose to buy one at a pet shop, avoid all the red, blue, green, purple, black, etc. colored bulbs completely, they make a lot of "Blue Daylight" Bulbs and "Red Infrared" Basking Bulbs, none of these are appropriate for a bearded dragon, only white bulbs.
As far as his leg goes, assuming that your long UVB tube is an adequate one that is mounted correctly, and that you haven't had him for very long to begin with, that means that he's got a potentially dislocated elbow/shoulder or a broken bone, either from falling off of something accidentally, or if he got his toenails stuck in something, like a hammock or some other piece of mesh or cloth decor, then he probably yanked his arm while trying to free it and he may very well have dislocated it.
He needs an x-ray done at a Reptile Vet ASAP, as if it's broken or dislocated it will need to be set properly, and he probably needs some pain meds, poor little guy. At his age he hasn't even begun to start growing, and will be doing so very shortly, they do almost all of their growth and development during their first year of life, so his arm needs to be properly set so it heals correctly and grows properly.