In a situation of great need, it is permissible to immerse with a piece of cotton coated in oil (preferably fish oil) or Vaseline, placed deeply into the ear.
If there is a serious concern about water entering the ear even with the cotton wool in place, one momentary immersion is sufficient. (If you are Ashkenazi and immerse only once, you should recite the bracha after the immersion.)
Please feel free to get back to us with any further questions.
Refuah Shleimah!