I'll give you my non-expert 2 cents here, but keep in mind - it's non-expert..
A Cochlear Implant is used only if you are completely deaf on both sides, but have at least one functional cochlea and cochlear nerve. In some surgeries, the entire cochlear nerve is removed from the AN side, so you can't use that one. If by chance, you lose your hearing on the non AN side, but the cochlea and cochlear nerve are still functional, a CI might be an option. There are many other variables that go into determining who is a candidate for one as well. I am not aware of any AN patients that have a CI (that doesn't mean they don't exist, I just don't know of them) - however, in cases of NF2, where the cochlear nerve is non-functional on both sides, there is an ABI (Auditory Brainstem Implant), which sortof acts like the cochlear nerve and sends stimulation directly into the brain stem, thereby bypassing the cochlea, which doesn't work.
A BAHA works by placing a small titanium screw into the bone behind your ear. To that, you attach a processor with microphones - the microphones pick up the sounds from your AN side, process them into sound waves that are transmitted through the bone and around into the functioning cochlea on your good side. If your hearing loss on your good side is due to something other than a poorly funtioning cochlea, this is still an option for you, but you'd need to determine the cause of your hearing loss on the good side first.
I don't know alot about TransEar, but I believe they use the same theory of bone conduction, but there is no surgical implant. I think it is worn in the AN ear, sound is routed through the bone again and goes into a receiver on the good ear. This is a good option if you don't want to go the surgical route. I decided against it because I have very small ear canals and can't stand anything in my ears so I knew I wouldn't use it. There are many people on the forum who have these and can probably explain it better than I did.
All of them have good informational websites that can probably give you more technical info and then maybe, armed with that info, you can present that to your doctor and see what he has to say.
I hope this didn't confuse you even more. Eventually, this will all seem like common knowledge - especially if you spent a long time researching your options like a lot of us did. But considering the majority of the medical field hasn't heard of these products, I guess it's only common to us!