Do your dragon a huge favor , take him to a reptile vet and have the injured arm assessed .
This will involve an xray. It's worth it and the vet will then be able to advise the BEST way to treat it if it's broken or there's a serious dislocation.
Thing is unless you are training in vet medicine and KNOW what you are doing, your mucking about with a make shift splint is very likely to do more harm than good and cause some very serious perhaps life threatening complications for the dragon , and will likely result in a serious infection, gangrene (necrotic tissue / bones) and a permanently crippled reptile.
PLEASE DO NOT RESORT TO HOME REMEDIES AND HOME TREATMENT if there is strong chance the arm is broken.
Vet visit is very much warranted if he's not using when you get up .
So your priorities should be , in this order :
1) dragon to reptile vet for examination and xray if the dragon is still not using the arm.
I can tell you first hand experience a skilled vetsurgeon can do wonders with broken arm or leg on lizard , even a juvenile lizard. My George the Blue Tongue Skink broke his left upper arm somehow (being silly and rambunctious I suspect) on day in his rearing tub. He was about 6 months old so not a really big boy , the vet after another vet told me it's nothing but a sprain , took xray and found a fine spiral brake in the big upper bone in his arm, so the decision was made with me to put him under a general and insert a custom made stainless steel pin to stabilize the bone , a special dressing was made and the arm and full shoulder immobilized with a special cast.
I was required to give George a combined IM injection that had mixed antibiotic & pain relief (which was good stuff as he got really perky after the injections) every 2nd day & calcium rich foods and a daily oral dose of CalciVet solution..
The cast came off several weeks later and he's been good a gold and you'd never know he has a broken arm .
2) show us the dragon , how heavy is he ?
3) show us the tank (we need to see the setup , substrate , lights and how you are monitoring temperatures.
4) basking spot temp, warm zone temp, cool zone temp ?
5) tell us his current feeding schedule and diet , and supplimentation schedule ?
6) tell us exactly what lights are currently in use (for basking spot (to provide heat + light) , UV , and their brands.
7) distance from the UV source to the basking spot ? , is the UV source naked or in a reflector (dome or hood) ? and is it on top of under the mesh lid ? )