And regarding strengthening the thumb: my thumb usually sits quite loosely on the neck, sometimes it even lifts off, or only the tip of the thumb touches the neck. Not sure how this would strengthen the thumb. So perhaps this is also part of my problem!?
Pain is a warning that something is wrong with your technique. I gave myself tennis elbow for a year because of over practicing barre chords. For me, the treatment was Trigger Point Therapy.