Does regret help us to correct our faults? Does regret / guilty help us to correct our faults? Isnt the pain from our faults push us to the correct path?
In the Abhidhamma, regret and remorse over the past is considered an unwholesome mental factor.

Worry (kukkucca) is remorse, brooding, and repenting over evil acts
done in the past or good acts left undone.

The following theme for reflection from AN 5.57 (quoted below) can prevent the arising of unarisen unwholesome states. It encourages shame of evil (hiri) and fear of evil (otappa), which are mentioned as beautiful mental factors in the Abhidhamma.
So, remorse and regret over the past is unwholesome. But shame of evil and fear of evil, or basically moral shame (hiri) and fear of wrongdoing (otappa), for the future, is wholesome.

“And for the sake of what benefit should a woman or a man, a
householder or one gone forth, often reflect thus: ‘I am the owner of
my kamma, the heir of my kamma; I have kamma as my origin, kamma as my
relative, kamma as my resort; I will be the heir of whatever kamma,
good or bad, that I do’? People engage in misconduct by body, speech,
and mind. But when one often reflects upon this theme, such misconduct
is either completely abandoned or diminished. It is for the sake of
this benefit that a woman or a man, a householder or one gone forth,
should often reflect thus: ‘I am the owner of my kamma, the heir of my
kamma; I have kamma as my origin, kamma as my relative, kamma as my
resort; I will be the heir of whatever kamma, good or bad, that I do.’

Hiri and otappa are explained below in Ven. Bodhi's &quot;The Guardians of the World&quot; :

The Buddha points to two mental qualities as the underlying safeguards
of morality, thus as the protectors of both the individual and society
as a whole. These two qualities are called in Pali hiri and ottappa.
Hiri is an innate sense of shame over moral transgression; ottappa is
moral dread, fear of the results of wrongdoing. The Buddha calls these
two states the bright guardians of the world (sukka lokapala). He
gives them this designation because as long as these two states
prevail in people's hearts the moral standards of the world remain
intact, while when their influence wanes the human world falls into
unabashed promiscuity and violence, becoming almost indistinguishable
from the animal realm (Itiv. 42).
While moral shame and fear of wrongdoing are united in the common task
of protecting the mind from moral defilement, they differ in their
individual characteristics and modes of operation. Hiri, the sense of
shame, has an internal reference; it is rooted in self-respect and
induces us to shrink from wrongdoing out of a feeling of personal
honor. Ottappa, fear of wrongdoing, has an external orientation. It is
the voice of conscience that warns us of the dire consequences of
moral transgression: blame and punishment by others, the painful
kammic results of evil deeds, the impediment to our desire for
liberation from suffering. Acariya Buddhaghosa illustrates the
difference between the two with the simile of an iron rod smeared with
excrement at one end and heated to a glow at the other end: hiri is
like one's disgust at grabbing the rod in the place where it is
smeared with excrement, ottappa is like one's fear of grabbing it in
the place where it is red hot.

And from Iti 42:

&quot;Bhikkhus, these two bright principles protect the world. What are the
two? Shame and fear of wrongdoing. If, bhikkhus, these two bright
principles did not protect the world, there would not be discerned
respect for mother or maternal aunt or maternal uncle's wife or a
teacher's wife or the wives of other honored persons, and the world
would have fallen into promiscuity, as with goats, sheep, chickens,
pigs, dogs, and jackals. But as these two bright principles protect
the world, there is discerned respect for mother... and the wives of
other honored persons.&quot;
Those in whom shame and fear of wrong
Are not consistently found
Have deviated from the bright root
And are led back to birth and death.
But those in whom shame and fear of wrong
Are consistently ever present,
Peaceful, mature in the holy life,
They put an end to renewal of being.