Tail injury, i'm trying not to panic

Our littlest girl, Edwina, just got her tail cought in the hinge on the
cage....she squeaked the freaked and jumped/ran away....leaving the tiny tip
of her tail in the hinge, along with a long white thin threadlike piece.
It's bleeding, but she seems to still have full function of her tail, she's
wrapping it around my fingers and such as i'm holding her checking her out.
Will this scab over and be ok? Should i be doing something more for her? The
other two girls are also grooming her and they're eating together as
well....

This JUST happened, 10-15 minutes ago....i'm trying not to freak....she's
just boppin around like nothing's happened...should i be doign the same?

Thanks,
A worried Mom
Joy

P.S. Edwina is our newest addition...she's an adorable charcoal and white,
stubby nose, and long silky hair....

Try and keep it clean, and a tiny bit of antibiotic ointment is a good
idea if you have it. It's pretty easy for mouse wounds to get infected
(as every room in a mouse house is a bathroom). If it's clean, it
should be fine. Just check for swelling or discoloration untill it's
healed.

I adopted a boy last month from Petco who had had the second half of
his tail amputated, as it got infected after too many fights. I named
him Shortcut.