Is it permissible for a girl to go to the doctor and buy skincare products without the knowledge of her mother, who objects to it, and would she be considered disobedient if she did so?

Obedience to parents is obligatory in matters that benefit them and do not harm the child, and in matters that benefit the child and do not harm the parent. Therefore, disobedience is not forbidden if the parent prohibits it. If going to the doctor or using skin medications is beneficial and does not harm the skin, then obedience to the mother in refraining from it is not obligatory. However, honoring the mother and treating her with kindness is obligatory. One should try to convince her, seek help from those who can do so, or conceal the matter from her as much as possible.