Hello Katie,
you have every right to use the women's locker room, but I understand it makes you uncomfortable if you have the impression people "clock" you. Do you have the support of the management to use the women's locker room? While I don't think you should feel you have to discuss this with them, it might be reassuring for you to know that they will handle this professionally.
Also, do you have a female friend that you could go to workouts together with? Maybe it'll help you to feel a bit more comfortable and confident there. Locker rooms are truly terrifying!