As far as the single sided deafness. Look into a BAHA. I am also single sided deaf and got a BAHA about 6 months ago. It doesnt sound as "nice" as regular hearing but now I can hear on that side. One of the nurses in the PACU during my recovery from the implant stage of receiving the device had one and told me I was going to love it and she was right!
I have been single sided deaf for ten yrs and with time adjusted very well to this kind of hearing loss. No one ever knew unless I told them. For me the main issue was I was always getting a cramped neck. And occassionally someone would whisper right into my deaf ear and of course I could not hear that. But in general people dont go around whispering into your ear at work! In fact I dont remember that ever happening anywhere but in my personal life. I think this kind of hearing loss would be more of a problem if you worked in a big loud factory.
That said although with time you will become so accustomed to it, the BAHA does make things simpler. No more turning your head slightly to hear the person next to you talk when you are walking. I still do it automatically even though I can hear on that side now. People always tell me I am so attentive and I am! I really that there are very few careers that SSD(single sided deafness) would stop you from doing. If that did not happen too long ago I can guarentee you your brain with accomidate and that will get MUCH better. Although it may be years before you dont really think about it.
As far as the balance goes I feel your pain there. But dont borrow trouble. Right now you are just having little episodes of imbalance, right? Find out your triggers and avoid them like the plague! I had sudden sensory hearing loss and then residual balance stuff. A neurootologist, not just an ENT, is the one you want to see. They can do things for you that most ENTs dont even know about. As far as a little imbalance goes stop sweating if its not bad. This could be the worse it ever gets. Are you aware of how many people have little imbalance problems? Many many many. Heck, most people with colds and sinus infections get a little lightheaded periodically. If this is what you have join the club. Those of us approaching menopause would also like to welcome you. You may have it a little more often then most. Find your triggers and you may have it less then most that never had it as often as you.
If you have something like Sorgen's syndrome, think that is what its called, then you are going to have to plan carefully and try to get your clinical time in before the worse stuff happens. Although I know some of these syndromes can progress to be so bad you could not possibly work and in some vision is also affected, I would work as much as I could because at least you would then be able to collect more SSD and perhaps have disability insurance.
If you are having true vertigo spells you really need to get to a good doc. Even then that good doc will tell you that is rare to have someone who cant be helped at all with this problem. And generally this is a problem that goes into spontaneous remission quite often. Unfortunately, it can come back out again but by then maybe you wil have your experience. I have a friend that has it and he is one of those guys you see up in the buckets working on the lines. He has had to take a leave of absence a couple times but is still a bucket man. Easier for him though, he works for the power company. and they are cool about it From what I have seen/heard not only do the older nurses in our profession eat their young but the employers do too. Yikes! We must be tasty.
I can also tell you that if you actually have big problems with this the key is to find your triggers, just like migranes. Then avoid them like the plague. My neck was a big problem so I go to the chirpractor once a month. I know that menieres is progressive but if someone is telling you that you will eventually be a cripple from it , get somebody else. Menieres is extremely variable. It is true you may be down for a while but with this disorder you always come back, if you want to. Maybe with less of a functioning balance system. But remember even people without any balance nerves can walk, if they want to . Some people resign themselves to walkers and wheelchairs but rehab is available and works. You just have to reeducate your brain.
There are so many causes of dizziness. Menieres, benign paraoxomyal positional vertigo, basilar artery migranes, neck injuries (these nerves feedback to your balance system).
I too am not sure nursing is for me but for different reasons than you. Balance problems are a big problem but they also tend to be temporary. Most people have more problems when they dont work right then when they are gone. That said this can be very disabling, but again IF that happens perhaps it will happen LATER as opposed to sooner. Even with progressive problems the nerve will eventually die out and then you are just not as steady as most. That can take a long time though and prior to the nerve dying you can have periods where you are quite disabled. Obviously I have some experience in this area known others that have gone through it. I dont know anyone who is not functional but all of the people I have known were very motivated. Even if you loose a whole balance nerve on both sides you can still be retrained to walk so well that the only way a regular person could tell is if you stand on one leg for them!
So do not take any jobs working as a flamingo lawn ornament. Other then that do what you are capable of and its nobodys business what your health status is as long as you CAN do the job!