I know what you mean,
Myself09...I've had rheumatoid arthritis for many many years, and it has deformed my feet to the point where it gives me balance problems (it's kind of like walking with marbles taped to the bottom of your feet), but I have steadfastly refused to get a cane. Like you, if I really focus on my balance and where all of my body parts are, I can do better at hiding the issue.
I guess I've always ascribed to the "if you don't use it, you lose it" theory, plus I'm afraid that motoring around under anything less than 100% of my own power is somehow an admission of defeat. (I will say that I love having a shopping cart to help me around the store, as no one can tell how much I'm relying on it!)
I'm 52, and I wonder how old I'll have to be before I "give in"...since getting the RA at 26, I've felt "old" for a long time, but I'm nothing if not stubborn! The thing is, when I see someone with a cane or other assistive device, I would think it was silly for them to feel embarassed at needing help. I would be more likely to think "wow, look at what they have to deal with, and they're still out here plugging away--good for them!", and yet, I have the same embarassment you speak of, and I've often asked myself why...vanity?