if its a racerback then you might be able to take an inch off of each shoulder by sewing it right where the seam is!
Definitely try wearing a bandeau or a Cami underneath it. They have really cute ones with lace and all different colors now, just stop by a Forever 21 or maybe even the American Eagle you went to, Charlotte Russe or Wet Seal, they all have cheap solutions to your problem. (:
Stop by forever 21 and grab a cute bandeau (they're super cheap there) if you want something with straps get a bralette. They sell these in Victorias secret and pink
Find a color that compliments the color of the tank you got and get a sports bra in that color that compliments it (preferable a sports bra that doesn't have a low cut either, then it will hopefully cover up what needs to be covered) so just wear it under the tank. Sorry if it doesn't look good but in my head it should and that the only thing i can think of.
