I know candies and SO brand brad tend to run a bit small, maybe try those? But if you're a double A you might be able to get away with going braless or just wearing a bandeau instead depending on the top you wear.
If you're smaller than a 32A you probably don't need a bra quite yet... Try a sports bra if you really want but don't jump into that yet because once you need bras it's a pain in the ass. If you really want something to cover up try a cami with the built in double layer around the chest area