I played a teifling actor who would wear makeup and shave his horns. (And wear hats or goggles to hide the nubs)
Probably a lot of ways to handle it. Tell people "This is why you don't mess around with magic" and point to your face. People will assume that a spell went awry and made you that way.
When people accuse you of being a demon, you could act confused, and then pretend to freak-out when you see your reflection in the mirror/glass/water. Then you desperately ask the person who pointed it out to help you until they go away/give you money.
You could act SUPER suspicious, like, suspiciously suspicious. Tell everyone to look at you and focus on you, and make them think that you are some sort of distraction. They'll rush back to their homes to make sure they're not being robbed. Especially good when you're escaping. "Yes, everyone, come, follow me... into the darkness of the woods..." I know i wouldn't follow after that guy, he's up to something.
You could tell them that you had an exorcism, and apparently this happens sometimes. Demon on the outside is better than demon on the inside, or so the cleric says.
Convince an ally to get a face-tattoo. I'm sure 50% of the questions you get will be redirected to that guy. (Worked on Baccano!)
Insist that the other guy looks like a demon, and that you look normal. This one only works if you're alone with one guy, or gullible groups.
Buy a disguise kit, and put some poor-quality demon prosthesis on, like vampire teeth and papermache horns. People will think its just a poor quality costume, and if they ask you about it, you can just take out your fake teeth and say "See, costume."
Convince your whole group to go with a "Demon-Theme," and wear red and fake horns. People will just think you're the most diehard cosplayer of the group.
Constantly be promoting a Carnival that is coming to town, along with other "Freaks." When someone yells that you are a demon, shout out, "Rawr! I am the Demon, come see me at the Goldshire Carnival, alongside the one-eyed man and the bearded lady! Only two copper! Petting zoo for the children! Rawr!"
Or do what I screamed into Frankenstein the first time i read it, which was: "Wear a mask, you idiot, so they can't see your awful, awful face..." Frankenstein's monster coulda saved alotta hardship with that one. Just tell them you're terribly disfigured and can't take it off.
