Make shure that your fretting hand fingernails are as short as possible. Then, for chords, put the fingers very steep on the fretboard (ideally 90 degrees) to make shure to NOT touch the adjacent string. For some chords, you can use alternative fingerings. For example: Do you play a simple open A chord with 1-2-3 ? I bet that 2-1-3 is better for you!