Son fell off bed 3 days ago finger is swollen at tip and very bruised under nail. should i have it drained. he is 4?

Get it checked: Your son probably has subingual hematoma from the injury. If the area involves less than ~25% of the nail bed, and is painless, it should resolve in a couple of weeks without any treatment. If the bleeding seem to involve a larger area or the area is painful, it needs to be evacuated by a procedure known as trephination. In the meantime, soak the area in warn water and use ibuprofen for pain.