I am sorry about your poor dog!
The boil that you have described sounds like a draining tract from a granuloma or abscess. Serious infections that cause severe swelling and draining tracts can be due to a foreign body that has entered through the nostril and migrated via the sinus's to your dog's forehead or through a penetrating wound into your dog's forehead and knee. They can also occur from many bacterial, or fungal infections.
Since your dog has been on antibiotics already with no improvement than,
1. the infection is not a bacterial infection, or,
2. the wrong antibiotic was given, or,
3. the correct antibiotic was given at too low a dose or for too short a duration.
If it is not a bacterial infection than it could be a fungal infection. Common fungal infections that cause granuloma's and draining tracts include: Cryptococcosis, Nocardiosis, Coccidioidomycosis, Histoplasmosis, Aspergillosis, and others. I don't know where you are writing from but some of these infections are regional and others are worldwide.
It would be best to identify the infection with a biopsy and a fungal, aerobic and anaerobic culture and sensitivity from an uncontaminated sample. Then the correct anti-infective can be started immediately. Some of the fungal infections require oral anti-fungal medication for months to years! But, once treated should not create any more problems for your dog.
Granuloma's often must be surgically removed. That abscess you described may need debridement and deep flushing, or surgery.
Lastly, there is one more cause for the lesion you have described and unfortunately it is cancer of the dermal tissues such as Squamous Cell Carcinoma. A biopsy is necessary to for definitive determination.
Please give us an update when you can!