Yes a perm can possibly change your hair permanently in some cases.
When you get a perm heat and chemicals are used to give your hair the perm and those chemicals and that heat can change the structure of your hairs follicles permanently.
The chemicals reconfigure the protein bonds in the strand and hair follicles as well as break them down which can permanently change your hair.
This is especially true if you got the perm when your body is about to experience a hormonal change.