The orange liquid ( colour of weak tea ) is likely betadiene ( iodine ) in the bathing water. Worth a call to vet to find out.
If you have a small food tub , something about the size of a take away plastic tub is perfect for a little hatchling like your's.
The weak betadiene is very likely to help reduce the chance of the breaks in the skin becoming infected.
Just be aware that betadiene as well as killing bacteria , also kills newly granulating soft tissues like skin and subdermal tissues. ( This is something I was told by a specialist wound care nurse practitioner when I was having surgical injuries in my lower left leg treated , and pressure ulcers treated .)
I'd recommend F10 Antibiotic Barrier Ointment as a better solution on the external injuries.
The antibiotic injections are to kill the very likely systemic infection in the vent tissues and blood stream. The betadiene solution wont help with fighting that.