I have a CI for single sided deafness. (One ear functions normally) The fact that you have memory of hearing in that ear is likely to benefit you if you do go with a CI. I have been working with a CI implanted as an adult for my right ear and have not had hearing in that ear from a very young age, if even then. It is likely that your brain will adapt. I have gotten much further than my doctors thought possible without memory of hearing on my right side, but I am still working on it since my brain does not have the memory of hearing on that side.
Also there are different programs you can work on to fine tune your hearing and help you adjust mentally to new sounds with a personal audio cable that you can connect your CI and computer with.
Just a couple of things you should probably know before surgery. You will need a couple of shots before surgery to prevent a disease that can affect how well the implant works and the surgery is not when you receive your new hearing, it is often called phase 1 for a reason. After surgery you will be given a few weeks to a month to heal before getting your outside processor (what appears on the outside of a CI) and when it is turned on (the process is called activation) you will start to get new sounds. Any further adjustments are usually referred to as mappings by your audiologist.