Wearing a bra that's too small will cause fat to be pushed out on the sides but does not cause an increase in the amount of fat stored in the underarm area. If you have an accumulation of fat in the underarm area that makes you self-conscious in sleeveless clothing, liposuction will be a solution for you. In the future, other non-surgical options may be available, e.g. Kybella injection, which is currently FDA-approved for permanent reduction of double-chin fat, MAY be an option if this indication receives FDA approval. Please consult with a board-certified dermatologic surgeon who performs tumescent liposuction to explore whether what you have is fat and is amenable to liposuction.