I understand your predicament. There is a tube called the Eustachian tube, which connects the middle ear with the nose and the throat. Whenever there is a cold, the infection in these two places reaches the ear easily. This may cause some mucus to collect inside the middle ear. Such an event reduces the free mobility of the eardrum and results in a hearing impairment. However such collections usually resolve in a few weeks completely. Occasionally the mucus collection gets thick and refuses to go away. This disease is called a glue ear. In such children, a small incision is made to drain the thick fluid. To prevent further recurrence and to ensure equal air pressure on either side of the eardrum, a Teflon plastic tube is inserted in the eardrum. This tube is called a grommet because of its shape. Usually the grommets stay in place for a few months to a year at the maximum, after which they get extruded. When they extrude, they may have to be reinserted.
The adenoids are tissues similar to the tonsils. They are situated in the highest part of the throat right behind the nasal cavities. They enlarge during every episode of cold and become normal when the cold resolves. Because of their situation very close to the Eustachian tube, the tube gets blocked when the adenoids enlarge. This results eventually in a glue ear. In selected children who have a severe degree of nasal obstruction due to adenoids, surgical removal of the adenoidal tissue is also done at the same time as insertion of grommet.
After insertion of a grommet, whenever there is another cold episode, obviously the mucus discharge will again reach the middle ear through the Eustachian tube and this time, it will drain through the open grommet. Another common cause of ear discharge in a child with grommet is getting water into the ears, during bathing or due to soaking in rains. This may lead to an infection and ear discharge may ensue. Depending on the severity and the nature of the infecting organisms, the discharge may be blood stained. When the infection progresses, there might even be pain. This is one of the expected outcomes. The ideal treatment is prevention. But when it has occurred, meticulous cleaning of the ear and a few eardrops will resolve the problem totally. The drops that you have mentioned (Sofradex) are fine. However, as with every other antibiotic, you may need to change the same depending on the clinical outcome. Cleaning the ear is as important as the instillation of the drops. Quite obviously, any cold will have to be treated simultaneously. Such a treatment will resolve the issue completely.