My only advice is to take a deep couple of breaths and remind yourself that your academic advisor is there to assist you with school. They are not there to judge or hurt you. They are there to help you become educated and trained.
I would caution oversharing. Certainly make this person aware of your situation, but they are not in the mental health field. They are not trained to deal with anything besides academics. You might want to stay focused on what specifically you need to get through school-wise ex. time off for your mental health lasting (blank) amount of time. What forms need to be filed? When and where?
Also, remember in the USA you are protected legally as diagnosed mental illness qualifies you for reasonable accommodations under American W Disabilities Act. I know because I have done this exact same thing only i had to call my Department Chairman for grad school at home at night. Not fun. i was so nervous. I couldn't take my final comprehensive exam for the degree because of severe depression and anxiety.
But i did the above. I took some breaths, explained the situation without too many of the gory details, assured her I could produce documentation from Psych dr and therapist. Then, I told her what i specifically needed, which was to remain in school, but sit for the exam the following semester.
She agreed, said not to worry, told me what to submit and where, and told me to feel better.
I took the exam the next semester and completed my Masters degree. One of the best academic decisions I ever made was to make that call.
You are taking care of yourself. You are making the right call too.