My 4yr old landed on my 2yr olds finger and immediately the tip started to fill with puss. It looks like her finger nail will fall off, what do I do?

Go see your doctor. Well go see her doctor. Ideally, should go to urgent care or er to make sure nothing else going on, eg broken bone (fracture) or dislocation. Pus represents infection which we wouldn't expect immediately upon trauma/injury. However, it's possible to bleed under the nail causing it to separate. We can poke a hole in nail to release blood & bring relief so take her to doctor as soon as possible.