Why does my pugs muzzle stay red?

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I have a 3 year old pug named Binky. He lost all the fur off his muzzle and it stays red, even though I clean his face every day. I just wipe his face with a warm, damp paper towel, because he's allergic to a lot of stuff. He also has an ear infection and I have to treat it twice a day. Could that be why his face is red? I have to really hold onto him to treat his ears because he tries to bite, so I know they are sore. :( Does anyone have any suggestions, or know anything about pugs?