First of all, please take a deeeeep calming breath...then slowly let it go. Try another one or two, as they will help to center you.
In answer to your question, yes, I would recommend your using a cane if you are unstable on your feet. I use one and I can't tell you how many times it has saved me from toppling right over! And you can find pretty and stylish ones on the net. This is a company that I have done business with and they were prompt and professional in getting my canes to me. http://www.fashionablecanes.com/?gclid=Cj0KEQjw1pWrBRDuv-rhstiX6KwB...
They offer some nice canes.
EBay is another good place to find them. I just looked under "aluminum folding canes" (without using the quote marks) in eBay and found some very attractive ones. I have also found the canes with the cushioned handles to be more comfortable than those with wooden handles.
What will people think? Well, it seems like they are behaving poorly currently, so it doesn't sound like you have much to lose by using a cane. I always refer to mine as a fashion accessory, and have bought enough of them for it to be so. Raise your head in pride. You are a woman with a legit illness. You are a strong person to handle it and those who pooh-pooh you are ignorant. I doubt they could handle what you are handling, and not with good grace either. If someone blows up to me with an attitude, I am going to tell them that I have leprosy or something, to get them freaking out yet showing some respect, LOL! No, probably not, but I'll be sure to tell them that I have an autoimmune disease that has made my body very ill and weak. If they don't like it, Phooey on them. Walk on by, to quote an old song.
In regards to your teachers, is it really their place to pass judgment upon you if you are doing well? I personally think not. Telling an employer upfront might be another matter but that's another topic for another day. I personally think that as long as you can hack the studies, your teacher doesn't need to know about your illness, unless you want to tell him or her.
People have been very kind to me ever since I started needing the cane. I don't look as young as you but I've been told many times that I look like I am in my 30s...the point being that looking or being young doesn't necessarily sign you up for meeting rude and thoughtless people all of the time. I do find that being in good cheer makes others more comfortable around me. I always smile at kids who stare at my cane and even talk to them a little about it. You have an inconvenient illness, no more.
Hugs to you. I can see that you are very nervous about your future with fibro. Just think of yourself as a normal person who needs more time and rest. And allow yourself the luxury of using devices that will aid you, especially if they will keep you safer. Good luck, kiddo!