Strapless bras are often a disaster. I spent an entire work shift the other day pulling it back up after it kept falling down underneath my dress. And no boob size doesn't seem to relate to holding those things up.
Then we have the stick on bras. Silicone or fabric. Most people have given this a go for their backless dresses, and they work for a while.. sort of. Firstly if you sweat at all you run the risk of your stick on boobies just falling off completely. If your dress has cut out sides you may not even be able to position them so that you can't see them, which is annoying as hell. They make your boobs look odd shapes as they sit awkwardly on top. Worst of all they don't even come in many sizes. The largest being a D cup, but I can hardly find them, as most stores only stock up to a C.
Enter Nipple concealers or covers. I only just discovered these and man I have been free boobing it half the time now. These little silicone covers are reusable, and in the shape of like a squished flower. They are super cheap, and you can wear them under anything. Obviously they don't offer any support, but girl you are young and you rock those strappy and sheer dresses!
They are usually quite cheap to purchase as well, so I completely recommend giving them a go!
Nipple Concealers - Cotton On Body $6.95
Nipple Covers - Bras & Things $14.99