Injecting pain relief to a dragon.
Above the kidneys is the key.
I was told by my reptile to choose location on the back near the shoulder blades, and carefully between scales and just under the skin - really a two person job , one to immobilize the lizard , other to handle the needle and syringe.
https://www.youtube.com/watch?v=OKwv88nTlx8
I expect the syringe supplied by the vet will be mixture of pain relief & antibiotics and you'll need give an inject every other day or so to help the dragon with pain relief.
I'd have the dragon on a few layers of clean kitchen grade absorbant paper towels and i'd be removing all opportunities to climb (other than the hide's top) , and replace the paper as soon as you any excrement or exudate on it.
F10 antibiotic barrier ointment is what is needed to keep the wound infection free.
Very important to keep him warm 24 hours / day while the wound is healing , this will help boost his immune system and help him fight off any infection due to the original infection or post operative infection.
Careful of the site turning septic , there doesn't appear to be a drain or a sterile wick there to allow it to drain while healing - if an abscess forms inside the site ( due to the site be stitched closed) this can result in a nasty systemic infection.
The blanket is probably not a good idea as it will harbor germs unless you sterilize it every day.