Thanks for your question.
It sounds like you might have otitis externa- which is a infection of the ear canal. This will not improve with the treatments you have done at home.
This is really common. It tends to follow after swimming, but it can occur even in people who vigilantly keep their ears dry. In the meantime, do not put anything inside your ears. You need to make an appointment with your regular doctor for some antibiotics- I use cortisporin otic.
I know what it is called, but it never seems to clear up. Next time I have to go to the doctor, will ask her for a prescription as you have suggested. Will look it up first since I do not like taking antibiotics unless I get a chest infection.
The prescription is for ear drops, it is not a systemic antibiotic like the ones you get for chest infections or urinary tract infections.