BLUE TONGUE SKINKS

So first off a bit of back story.
I had received my BTS 8 months ago as a rescue. The previous owners were out of town a lot and she was neglected and under weight.
After a first few rocky months I got her weight up and she's become a wonderful snuggle bug.
I pay close attention to her sheds as I am aware of gloving and toe loss. I never saw any problems with bad sheds or build up so I'm baffled as to why this toe has turned black and is separating from her foot. She hasn't changed her eating habits or temperament.
So, do I just let it run corse? Is antibiotic ointment ok to protect the open spot? I'm afraid of infection setting in. Never had to deal with toe loss before.

Looks like it might be an IJ...?
And, yes, that toe will be lost. I'm betting he could stand his humidity being higher in the tank, either that or have access to a humid hide.
Unless you see redness spreading on the rest of the hand/arm, they usually handle the loss of one toe just fine. If you want to put a Betadine solution (10 parts water, 1 part Betadine) in a cup and try to hold his foot in it for a while each day would be fine. I try to avoid putting anything on my skinks that isn't reptile specific or cleared by a vet, but I have heard others say they put Neosporin on their skinks just fine. Up to you.

Good luck with your BTS