Dogs have a pinna (fleshy and cartilaginous ear lobe) but birds do not. Dogs get yeast/bacterial infections (similar to those affecting ladies) that can often be treated topically but birds do not have anywhere close to the same anatomy (basically a hole in the skull covered by a little skin and feathers). Obviously digging around in there would not be a good idea nor will topical meds penetrate that big of a swelling (even oral or injectable meds might have trouble). Antibiotics may help, even if it is only treating a secondary bacterial infection. If the primary cause is protozoal you’ll need to treat appropriately. Is it an abscess? Could you hot pack it twice daily to encourage it to rupture? Could also be secondary to a foreign body (thorn etc. poked in there somewhere). Another possibility is osteomyelitis (bone infection), if it is hard and bony feeling throughout that could be what it is (very hard to treat).