A transformer works with AC voltages. You can't step up the DC voltage of the battery with one directly: you must first chop the voltage on and off, to give a 'pseudo AC' voltage, as is done in switch-mode power supplies (SMPS). Producing an SMPS only 3 x credit-card thickness is a tough challenge and maybe beyond the capability of a hobbyist. Even obtaining a small enough inductor and capacitors may prove tricky. If you found some way of deriving 15V, how much current are you hoping to draw (which would help us to determine if the project is feasible)?