I think your problem might stem from your technique, try this it might help, hold down a few easy chords, make sure you are placing your fingers as close to the fret wire as possible, also make sure your forming a good arch so that your fingertips are actually holding down the the strings. Now, remove your thumb and press down gently on the fretboard. This is just the right amount of pressure you need to play any chord. Practise on a few chords, Then place your thumb back on the neck, remember your thumb is really only a guide, keep your hand relaxed, this removed the soreness, along with fret buzz and muted strings for me. Good luck.