In regards to service dogs in general. From my understanding, the handler must be (legally) disabled to qualify. You cannot self claim a disability, or decide on your own that you need a service dog, at least not that would hold up in a court of law (as far as i know). There must be a medical professional involved that more or less states that you have This Thing going on and that That Thing is something you are unable to do so a Service Dog trained to do This Thing for you is medically required. Or something along those lines, but you get the general idea.
The dog must also be specifically task trained for your disability - meaning it does something for you that you cannot do for yourself and makes your daily life overall better. A good example of this is a guide dog for the blind. Seizure alert dogs for people with epilepsy. Other tasks can include: hearing alert for the deaf, mobility assistance for those in wheelchairs or with muscular/skeletal disorders, and so on. No other training is TECHNICALLY required, though i don't see how an actual service dog can be in public without at least the basics.... but maybe that's just me?
My RECOMMENDATION for anyone looking to use an existing personal pet as a service dog (as opposed to obtaining one already trained) is to put them at LEAST through Canine Good Citizen training just to make sure they're properly trained for public work. In addition to, of course, the task training. Certainly doesn't hurt to be CGC certified.
So, if you haven't yet spoken with a medical professional then I would say that would be your first step. See what they say about using your dog as a mobility support dog. You do not have to be mobility impaired 24/7/365, either - if you have "good days" and "bad days" that still counts. Your doctor should have no problem backing you up if you genuinely feel that having her as a service dog would make your life easier, especially if nothing else has helped in the past. Once you have their backing and support.... you're technically good to go, i think, at least in regards to the law intuit respect.
She already helps you with getting back up, and braces you when you're having difficulties, correct? That's technically her being task trained for your medical disability and that would be the answer to any questioning someone could legally present you. 1) Is your dog required because of a disability and 2) what task is she trained to perform for you - "She is my service dog, i have a disability - she helps me with my balance and braces me when i start to fall and helps me get back up if i do". You could also, if you wanted, take it even further and train her to retrieve items for you so you don't HAVE to bend over to pick them up - thus reducing the chance of a fall and eliminating the need for support when standing back up. That counts as well.
As far as people looking down on you... even if you had a big "i'm disabled" sign on your back, and you were in a wheel chair or had walking aids or something obvious people would still judge you for something and make excuses. Oh, they have walking aids, they don't really need that dog - why does someone in a wheelchair already also need a dog - they're not blind, they're moving too easily, they have to be able to see something.... It's unfortunate but that's just how some people are.
I know it's easier said than done, but.... if you need the dog, if you're doctor agrees, and the dog IS doing something to help you then i would just try to ignore everyone else and just go about your business. Going through the right channels means you're legally protected. What someone thinks isn't really going to matter. You do you.