~がる is used to describe third person's feeling but today I found this word "強がる私" I don't know why 強がる is used with first person like 私.
Is it because the speaker speaks in other point of view ?
If there is a reason, you can safely use がる for a first-person subject, because the basic meaning of がる is "to show signs/indications of ～". See:
Here 強がる is basically a lexicalized verb and thus has a negative overtone, but this がる still means "to show signs", and there is no reason you cannot use it with a first-person subject.
強がる is a word per se, meaning "to pretend to be tough"; I think it can be used also for first person.