Mine had a similar wound (she bit herself). Wound up getting some Silver Sulfadiazine, but that can't get in the eyes,
The neck is a tricky spot if, when retracting the head to hide, the eyes hit the wound, ergo the medicine (neosporin or otherwise).
Not saying to stop what you are doing, just check to see if it is getting in the eyes
When dry docking overnight in cold weather I have found it helpful to keep the bin off the cold floor (like on a table or something) and put some towels underneath and over the top to keep the warm air in - just have to be careful that the towels don't hit the light and create a fire hazard.
I have used the nocturnal lights, and they don't seem to cause a problem but for short term I had success putting some foil over the top and placing the regular basking light on top of it - it creates warmth without 24 / 7 light.
"I know up on the top you are seeing great sights, but down at the bottom we, too, should have rights"
~ "Yertle the Turtle and Other Stories" by Dr. Seuss ~