Dog's noses will peel much like people's skin does, although it takes much more severe sun, wind and rain to make it happen.
Bag balm is the best product for lubrication. Continue this and the vitamin lotions.
If there are wounds on the nose, you can clean the nose with peroxide or betadine and then apply some neosporin ointment. If this does not help, yu will want to see the vet for an antibiotic.
Aside from that, thyroid conditions can cause unknown nose problem so you will want to have your vet run a thyroid panel to rule this out. Some people have to go so far as to tattoo the nose to promote healing.
Keep in mind that contact dermatitis can cause some peeling as well. You should sanitize the dog bowls at least weekly and switch to ceramic dishes because they are less porous and less likely to hold bacteria.
Let me know if you still have questions.