Bit for horse with pink skin?

Have you thought about putting bit guards on to see if that makes a difference?

I've seen those and wondered if they were for that purpose or not.  I'll put that on my tack store list and give it a whirl   Thanks!

I use them on most of my barrel bits, they make some that just velcro off and on.

That sounds great

These work GREAT!!!!!!
http://www.thetackstop.com/easybuttonbitguard.htm
 
And these are just a tad thicker and work very nice too!!
 
http://www.thetackstop.com/cheekguard.htm
 
Hope this helps.
 

I've had trouble with plain snaffle bits soring the sides of thin-skinned horses' mouths in the past.  You may try the Myler type bits that have a bend at the butt of the snaffle to fit the natural shape of the horse's mouth.  I actually had good results with an O-ring snaffle when the D-ring style sored Shelly's mouth.  Here is what I thought was going on: with the regular D-ring snaffle, when I pulled the eft rein it put pressure on the right side of the mouth, basically the bit was pulling through, and the straight edge of the D is what was rubbing the corner of the mouth.  I eventually transitioned Shelly to a Tom Thumb style curb bit whose shanks flexed outward at the butts of the snaffle, and didn't have any trouble with sores on her mouth.

With Roxy the thin skinned Paint mare I could ride her in either a large-Dee French link snaffle or a mullen style/straight shank Kimberwicke or grazing curb bit, but not the D-ring snaffle.  In her case, I think the middle link of the French style snaffle took away some of the problem of the right side of the bit pulling on the corner of the mouth when the left rein was pulled (and vice versa).  Instead of pulling through, downward pressure was exerted on the tongue and jaw. She took well to the weight of the mullen style mouthpiece, but I didn't introduce it until she rode well off of leg and seat cues.

In the big picture, backing up a bit (pardon the pun) on your training and spending more time working on leg cues will spare the horse's mouth all around.  I used to be shy of wearing spurs but find that when properly used they are the best tool for getting a horse to be sensitive in the sides, so that a slight leg cue initiates movement and the reins are more of an afterthought.