Frankie, a quick note about that picture:

You can see that a fairly large piece of the fingertip is gone.
It will probably bleed a lot. I would just wash it (if possible), put a towel or trauma-pad on it and go to the ER. (Take the fingertip with you if possible)

If you're going to the ER with it, don't use antibiotic ointment or Betadine in the wound. It makes it harder for the ER-doc to asses and treat the wound.

The main reason they stated for applying antibiotic is that it prevents the gauze to stick to the wound, but that isn't really a priority if you're heading for the ER. They will irrigate the wound anyway.

Of course this changes if your in a survival-situation or if it's a minor wound. Then you give the final treatment of irrigation, desinfection (with or without antibiotics), primairy and secundairy dressing.