Just an indicative example.
Several years ago I rescued a juvenile water skink who was being attacked and chased by nextdoors cat from hell (it's a killer of birds, possums, frogs, lizards and anything smaller than it is and they let it roam freely outside 24/7).
I intervened when I spotted the little skink in a mad panic running onto my front lawn with the cat in hot persuit, I stepped in and had to kick the cat to get it back off and scooped up the poor injured tail-less terrified little skink and brought him inside and placed him in a spare cricket tub full of shredded soft nose tissue paper , and placed him in the ironing basking under a towel in the warmest room in the house to calm down .
I didn't expect him to survive the night, but he did. So very next day I found a local reptile vet and took him to be seen by the vet and assessed.
Poor little guy had a broken lower right jaw , with a nasty penetration wound to his right eye and the back corner of his right side of his mouth. He was as to be expected very scared of us.
Nonetheless the vet thought he had a chance and told me I could care for him if I was prepared for giving him intensive care while he was been treated for his injuries and any infections resulting from the cat bite/clawing and thought if he made it through the next week he had a better than even chance of recovering, though he'd be blind in the right eye and never survive being released back to the wild, the choices were he put him down or I care for him (I figured he deserved a chance at life (even if as captive lizard)).
There was no prospect of Wires taking him on , as there are no Wires carers in my area or within 2 hours drive and their focus is wild injured birds and marsupials ONLY.
So I brought him back home and set up a hospital tub for him on top of a 5W heatpad and set up a makeshift hide for him and bought some calcium and vitamin powders, a 5% UVB compact and reflector dome and some small crickets and mealworms and lizard pellets (vetafarm and repcal juvi beardie pellets).
I had to give this little 6g skink IM painkiller/broadspectrum antibiotics injections in his back near the shoulders every 2nd day (was terrified of impaling with the tiny diabetic needle every time !!!, I'd never given injections before and I hated inflicting more pain on him in the process), oral antibiotics 2x per day (he hated the taste of this stuff) using a syringe with a plastic catheter needle's plastic tube insert only (in the back corner of his mouth) and liquid calcium , and try to get him to eat some insects (his mouth was too sore to handle solid food so I had to squeeze out the insect "meal/goo" and give him this so he got some protein.
Seems little wild animals soon realise you are trying to help them and he became quiet tame within a week at which stage we thought his chances were good and we named him Lucky.
Injections lasted 3 months. Oral antibiotics 6 months, and he was recovering and thriving and growing and became a wonderful little pet lizard who was ubertame, very inquisitive and super affectionate. He never managed solid food, because his jaw was very badly injured so all his food had be liquid form or soft or a paste/slurry.
Unfortunately 3 months after having his antibiotics stopped , he had a sudden massive relapse and was dead the next day .... I was heart broken. Vet thought he likely had an abscess internally that was a reservoir for the bacteria from the original cat attack injuries and this was what killed him when it ruptured suddenly.
At least Lucky got 9 months of life he wouldn't have had otherwise and his life under our care was full of kindness and very rich. He has special place in my wife's and my hearts and memories and our memories of him are still greatly cherished even 6 yrs down the road. This special little skink was my inspiration to start keeping pet lizards again (this time as an adult (I'd had lots of short term pet lizards and frogs as a child) , and they have become my wife's and my choice of companion animals.
So, as you can see , recovery for a lizard is a long process, even in a young lizard, principally because reptiles have very slow metabolisms cf mammals , healing is very slow from injuries too. Plus they are very good at hiding the fact they are ill.
Keeping a sick / injured lizard warm at all times (including at night) is key to helping them recover as is giving them plenty of high quality insect protein and plenty of time to bask. This was the advice I was given by the vet when I was caring for Lucky.
Kudos to you for caring for your sick beardie , just be patient and keep up the treatment and you'll likely have a wonderful pet in the long run.
.... you must be chuffed 
