Hi S.,
Noah didn't have diaper rash when his first two teeth appeared, but I had read that it's a possibility. It seems like teething brings out all sorts of different troubles! I don't know about the apple juice - I haven't started juice yet for my little guy.
And about the pinching - my lands do I know what you mean!! Noah likes to grab and pinch and poke and scratch (I look like I got into a cat fight with all the scratches on my chest if I haven't been able to trim his nails recently). I've actually been looking into buying a nursing necklace for those exact reasons.
If you do a search online for 'nursing necklace', you'll find several different websites. Some have them more geared towards the nurse-er (I think that's what the baby would be called anyway! ;) ), and others are geared towards the nurse-ee (again - don't know if that works but that's the mom! :) ) that look a bit more stylish than, say, alphabet beads. Obviously, it would have to have a very sturdy clasp & whatever material holds the beads together, as beads are a definite choking hazard, but...maybe that's something you can look into!
In any case, good luck!