If you have tried everything and still it doesn't work than i would tend to think its not what you think it is- maybe there was a hair or string or fishing line and its now gone and your seeing the indent/cut from where it was... if not than you HAVE to remove it. If you walked into any vets office , a tech can and will help you snip it off. You CANNOT leave it there... you asked what antibiotics the chick would need if it loses the toe--- my question is where would you get those antibiotics?- because wherever you would get them from ie vets office , feed store, etc thats where they could help you remove the string / hair.
To leave it on there would be cruel and unusual - even if you cannot get it off yourself , you have to find someone who can.
a neighbor? a friend? a parent? grandparent? the mailman- --- someone will help you if you ask
Dont let the animal suffer