I am experiencing big toe swelling and it is full of puss around the nail

Paronychia: It is important for your doctor to incise and drain the collection of pus and take a course of antibiotics to help resolve the infection. If there is an underlying course for the paronychia such as an ingrown nail, that needs to be removed.

Ingrown Nail: Sounds like an ingrown nail, where part of the nail is pushing into the skin. Could the nail have been traumatized? This needs to be checked out by your physician or a podiatrist (foot specialist). Don't wait.

Paronychia: Pus around sides of nail indicates infection and need for antibiotics. Please see your doctor.

Paronychia: will need antibiotics and possible incision and drainage. please see your GP