The larger cage will help. Also make sure his/her temperatures and humidity are within the optimal range. It would also be advisable to provide multiple places for the snake to hide. Since the snake is feeding well it most likely is not trying to escape it's cage in search of prey. You need to make the snake feel as secure as possible so it does not feel the need to go elsewhere. Imagine being in an enclosure that you can see another place to go and having a barrier or mirror making you think you can get there but can not. This is an artifact of the captive environment that snakes and other Herptiles are not accustomed to and they really have no means of knowing why it is they can not get to where they want to go. You can also apply some hydrogen peroxide or better yet Betadine® solution till it heals. The places to hide are important for the snakes feeling of security and well being. You could also cover areas that would make the snake think it can get to another location.
He/She should be no worse for the wear in a few sheds as long as you correct the issues that led to the rubbing in the first place. Most snakes want to hide till something stimulates movement such as hunger or the need to thermoregulate. They do not waste resources for causal movement. Keeping this in mind and correcting what is making the snake go on the move will eliminate future problems with nose rubs etc.
Not always so simple. I have had more then a few nose rubs and mouth abrasions while working with snakes over the years.
Hope this helps.
>>My littleest black rat snake has been rubbing against his cage and now his nose is a little bit discolord and has some dead skin hanging off it. It is not bleeding and he is eating ravenously on pinkies. what should i do to correct the problem. He is is a larger cage now. Will it go away after shed?
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>>My collection
>>1.0.0 Normal Taiwan Beauty Snake
>>1.1.0 Normal Black Rat Snake
>>1.0.0 White-sided Black Rat Snake
>>1.0.0 Anery Corn Snake
>>1.0.0 Amel Corn Snake
>>1.0.0 Normal Common Garter Snake
>>0.1.0 Hypo Northern Water Snake
>>0.0.8 red spotted newts
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Roberts Realm Of Reptile Research
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Thanks,
Frank Roberts

I opened my mouth and out flowed a melody black.