Is it possible to fix this abscess without getting rid of my implant? (Photo)

Unfortunately, it is not possible and highly risky to save the implant.  A synthetic implant used in nasal augmentation that is infected, should be removed and the abscess drained.  You will need antibiotics as well. Several months later after healing is complete (preferably a year) autologous material (cartilage) should be used for dorsal and tip augmentation.

In rhinoplasty alloplastic (synthetic) implants should NEVER be used, neither goretex nor other materials, it is a great luck yours survived for 5 years.Now you have a more than serious problem, I'd say a terrible complication leading to disfiguration and a future uncertain repair. What is going on there is a total intolerance to the material, and extrusion of the implant, which subsequently is becoming infected.You must follow the advice of your new doctor, URGENT surgery to open that nose, do aggressive debridement asap of all affected structure, removing the goretex and thoroug cleansing and disinfection. Eventually leaving the nose partially open to allow drainage and discharge.The sooner it is done the less internal damage.Be prepared psychologically, your nose will acquire a grotesque deformity the next months, and changin one; only when settled you can initiate process of rebuild and repair, but this time with AUTOLOGOUS cartilage grafts, please, and only by a very very good revision rhinoplasty surgeon.