Is single sided deafness a disability?

Technically, yes: you do not have full use of your faculties. Whether this would count towards special programs, exemptions, and benefits is unknown. You might consult with the querying party, or with the physician that you’ve been seeing about the ear.

Check with a disability attorney.

Yes, you can’t localize sound without input from both ears (which can be dangerous). Having said that, that doesn’t mean you qualify for any benefits, you would need legal counsel. Tinnitus is only a disability when it interferes enough to make daily activities of living difficult. There are even a few cases of a person committing suicide they found their tinnitus so it can be very debilitating but that’s on a case by case basis.

I am an undergrad in communication disorders

If a person has a permanent of long term physical or mental impairment that significantly impedes their ability to perform 1 or more major activities of daily living (other than working), that person meets the US federal definition of a disability.

Major activities of daily living include functions such as caring for oneself, performing manual tasks, walking, seeing, hearing, speaking, breathing and learning.

Whether one has a disability or not often depends on their own perspective, others’ perspectives and timing. Sometimes the person themself does not feel they have a disability because they do not feel their daily functions are affected, but are perceived by others as having a disability.
It also depends on timing—a person might not be disabled at all in their home, social setting, school setting, etc, but might be extremely disabled dealing with fast food workers with noisy background environments- a situation someone with single-side deafness might experience.

Check out the Phonak wireless cros aid.

http://www.youtube.com/watch?v=t-wMCHsmr9Y

Here is an interesting new device available for people with conductive or mixed hearing losses, or single-sided deafness / unilateral hearing loss. I have not tried this device, so I am not endorsing it in any way. If someone does try it, I would be interested to learn of your experiences. Thanks!

The Phonak CROS and BiCROS system mentioned above are also wonderful technology – especially if there is some sensorineural component.