If you don't want a specific person to see your profile on instagram so you can simply block that person. Here are a few steps on how to hide posts from someone on instagram or How to block someone.
(1) Go to instagram and move to the profile of the person.
(2) Click on the three dots on the top corner.
(3) There you will see an option for block user.
(4) Click and confirm.
In these few steps you can totally hide your profile for a specific person.