The iron must touch you, carrying it around is fine. Look at Toot and his knife, it's a steel blade with a plastic handle, and he's carrying it around all the time. The gun should be fine, since the handle is probably covered in something other than steel. The button in your pants could be a problem, if you don't wear anything between it and your belly. Look at people who are allergic to nickel and the reaction they have, it would probably be at least as bad here. Though it's not too complicated switching out a button.
I don't see a problem with disguising iron. It's not a lightning rod for magic, it's an allergen to the Fae. Of course it could be that any number of Fae have a fear of iron and won't even try. A changeling might have less of a problem with that.
Now there is the whole thing about how far to the surface the supernatural part of these halfbreeds is. If she uses glamours all the time, she might be well on her way to fairydom already, and every time she uses a glamour, the gun on her side feels a bit heavier. At some point, it must feel like carrying a block of uranium around with you.