As long as the white part doesn't look cloudy or wispy, there's nothing to worry about. It's just scar tissue that the axolotl has grown while trying to regrow its lost toetip. Usually axolotls will throw up their food if they've eaten too much, if they're stressed, or if they don't like the taste. If constipation has been an issue for him, you should definitely get him onto another diet. Fasting him for a day or so wouldn't hurt either, just so he has a chance to pass everything before you feed him again. If he hasn't passed anything in a day, fridge him for about 30 minutes to an hour. This will cause his metabolism to slow, which will make him release anything he has in his bowels.
A good diet for axolotls that I've found is earthworms, shrimp/salmon/axolotl pellets, and minnows as a treat. The minnows help "grease up the system" so to speak, which makes passing things much easier. I would feed a minnow every couple of weeks, more often if the constipation starts again.
It sounds like there isn't an ammonia issue, so he probably scraped his toes on something. Definitely remove that rock, and look around for anything else in the tank that might have tiny cracks or sharp edges he might have gotten caught on. My own axolotl ended up ripping his tail on the filter intake one day. I made sure to put things around it so it wouldn't happen again.