This all sounds like an issue over nothing, and especially petty making an issue of her having to separate out her underwear, or her wearing a towel.

Perhaps her wearing a bra is a little inappropriate, but the rest of it is all perfectly normal.

Just remember that it's not her that decided to move in with you, it's you and your gf who decided to move in with each other, so perhaps a little flexibility and understanding on your part would aide the situation greatly