How can I manage my symptoms myself if I have a puncture wound?

Likely not-need help. Fever, pus from the puncture wound, swelling/redness that's worsening, pain that is unusual or out of proportion, bleeding, ...If in doubt , call your doctor. These symptoms may mean your infection is getting worse, and may require surgical debrided net or IV antibiotics.
Have it evaluated. Such injuries can potentially be dangerous as one may develop tetanus, or a number of other types of deep infections. Wounds resulting from human or animal bites may be especially prone to infection. If the wound was deep enough they may lead to bone infections. If you develop pain, redness, swelling or other signs of infection seek medical attention.