What can I do for my skin abscess without going to a doctor?

Nothing. Abscesses need to be opened, drained and likely followed up with antibiotics all of which should be directed by your doctor. I would not recommend home lancing of an abscess.
Abscess Treatment. An abscess is a tender mass generally surrounded by a colored area from pink to deep red. Abscesses are often easy to feel by touching. The middle of an abscess is full of pus and debris. http://www.webmd.com/a-to-z-guides/abscess#1.