You are allowed to use a mirror. [In Talmudic times, mirrors were used to cut hair so there was a concern that you might come to cut hair.]

Chapter 303 Section 1

Chazal said a lady should not go out on Shabbos wearing certain non-clothing items as if she needs to go to a mikvah, she might come to carry them.

Examples of this are pieces of wool or linen material placed in her hair.

Chapter 303 Section 2

Material tied around the neck, as long as it is not tight, is permitted to be worn since she can go to the mikvah.