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In a puppy this age, you really need to be feeding a complete and balanced puppy food. It should have the appropriate calcium and phosphorous levels. This is needed for the bones and growth plates to grow and close at a normal rate. If you take out sugar, you're removing all the carbohydrates. This will throw off the diet and make it protein heavy. In that case, we'll end up with calcium:phosphorous ratios that are too high. This can lead to joint disease as the dog grows. Hip dysplasia often times will develop because of a poorly balanced diet when a puppy is growing.
When it comes to mange, as long as we are treating with the appropriate anti-parasitics, it should resolve. The diet is just giving the dog calories and nutrients to repair the skin. A complete puppy diet should have everything needed for those repairs.
So, I would go with a good balanced puppy formula. There are many out there- Iams, Science Diet, Eukanuba, ect.
I hope this helps, let me know if you have any other questions.