In general, secret itself has this intrinsic meaning already and you can make it more clear with adjectives like private, exclusive, unshared etc. You can even say (one's) own secret.
A crowning paradox of the discourse on honest dissimulation is that one's own secrets are always in danger of being lost, and therefore must never be hidden too well.
Additionally, I will mention some alternative terms that is related to the topic:
Firstly, I would like to add the word personalia:
the accoutrements, concerns or intimations that are personal to one
Secondly, According to Goffman's Theory:
Stigma is defined as the "gap between what a person ought to be and what a person actually is."
Identifies two different types of stigma - discretable stigma and discredited stigma.
The discretable stigma can be hidden. A personal secret or attribute that is unknown to anyone, but the individual.
If the person chooses to conceal the secret from everyone, it becomes a total secrecy and it is associated with self-concealment:
Self-concealment (SC) is a psychological construct defined as “a predisposition to actively conceal from others personal information that one perceives as distressing or negative.” Self-concealment can be understood as an instance of boundary regulation in the maintenance of privacy.
Finally, there is a term called secret-sacred (also used as sacred-secret) which is a loan word or a translation from Australian Aboriginal English. It has religious connotations but it can be applied to the secrets that is sacred to you and to your own life and culture. Though "secret and sacred" is a more common usage in English and in this sense.
secret-sacred (not comparable): In Australian Aboriginal culture, restricted to initiated men, or to women; not public knowledge.
From the book "Australian English - The National Language" By Gerhard Leitner: