I often smile at strangers as I walk around. Sometimes I get glares, usually from females who think I'm somehow hitting on them. Most people ignore me. A few people smile back. At one point, it occurred to me that people must think I'm mentally retarded, because if you look at most people, few if any smile at strangers.
It sounds like you have a low self esteem ( I do, and you sound like me) and are afraid of rejection, and a smile is a bit of an invite, and if not returned, you feel rejected.
Don't think of a smile as an offer, don't expect anything in return, don't think of it as rejection if they don't smile back.
Think of your smile as a gift, a free souvenir to anyone who wants it. Those who smile back accept your gift, those who don't just might have things on their mind, or might not trust a free gift from a stranger, and that is their loss.
You can't control how other people feel or think, you can only control yourself. Have fun with it, see how many people you can get to smile back at you.
As an aside, no one cares about braces, don't let them deter you.
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