Aloha! You're speaking with Dr. Michael SalkinI applaud your concern for your parent's budgie, Sarah. You've described a sinus infection that has become severe enough to erode through the skin above the sinus. This is best addressed with systemic antibiotics prescribed by a vet experienced in treating birds. Over the counter antibiotics designed to be placed in pet birds' water aren't expected to be drunk enough to be of value. A liquid antibiotic such as enrofloxacin, tetracycline, or chloramphenicol can be administered by eyedropper for a period of 10-20 days in order to eradicate such a stubborn infection as is seen in the sinuses of these budgies. Please call your local veterinary association for a list of avian-oriented vets in your parent's area or perhaps google "avian veterinarian/(your city)".Please respond with further questions or concerns if you wish.