Quick tip: bra extenders
Good quality bras are expensive, and if you're rapidly losing weight, you may not want to invest in bras that you may only be able to wear a few months. One option is to intentionally buy a bra that's a little too tight around the chest, and use a bra extender for a few weeks until you lose more weight and/or the bra stretches out a bit (which they all do).
Search on amazon or any lingerie shop for "bra extender". You can get them in 2-, 3, or 4-hook versions, and in a variety of colours. While they are a useful temporary solution for a slightly tight bra, I wouldn't use them long-term or with a bra that's more than just a bit too small. Better to invest in a properly fitting bra.