Thank you for the additional information.
There are several common conditions that can cause ain near the eyebrows associated with swelling. It is most often associated with inflammation of the frontal sinuses, which can be from an infection or non-infectious inflammation, such as allergies. Although less common than sinus disease, another common condition that can cause these symptoms would be related to spasm of the muscles under the skin. Conditions inside the skull can cause headaches in this area, but would usually not cause visible swelling and usually would not be affected by the application of ice.
You have been tried on several medicines that would help with sinus disease, including antibiotics and steroids, as your doctor has been treating the most common condition. When the usual first-line medicines are not effective, it is appropriate to perform an imaging test that will show the sinuses, such as a CT scan of the head. The doctor is usually more interested in what it shows about the sinuses, although it will also provide information about the brain. This will help to identify whether there is a sinus infection or inflammation that is simply stubborn (in which case, similar but stronger medicines may be needed), whether there is an anatomic condition that is preventing healing, such as a growth in the sinuses, or exclude the sinuses as a source of the headache.
If the sinuses are normal on the scan, then it would be appropriate to consider the muscle spasm as the most likely cause. A non-steroidal anti-inflammatory medicine may be helpful, such as ibuprofen or naproxen, but many people have already tried these medicines even before going to the doctor. Adding a muscle relaxer, such as Flexeril, may be able to help ease the symptoms. There also are various medicines that can be used chronically to help prevent headaches from muscle spasm, including certain antidepressants, such as amitriptyline or duloxetine, and certain anticonvulsants, such as gabapentin or pregabalin.
So, your doctor is on the proper track in performing the scan, which will help to elucidate the health of the sinuses, and if normal, it would be appropriate to consider muscle spasm as the likely cause.
If I can provide any additional information, please let me know.