I am not familiar with these verses. But I do have three hymns for "O Mother of Perpetual Help" these are found in the Manual of Select Catholic Hymns which was first published in 1885 and again in 1925. The hymn book was compiled by P. M. Colonel, C.S.S.R.

One of these melodies was recorded on The Catholic Devotional Hymns website:
https://www.catholicdevotionalhymns.com/recordings/2022-mission-church/

A few other options, won't vouch for quality.

Mary, Dearest of All Mothers - Eleanor Donnelly, Mount Mary Hymnal no. 69
Hail, Sweet Mother (O sweet Mother, ever help) - Cleveland Diocesan Hymnal, p. 39

And then there are hymns to Our Lady of Perpetual Succour (alt. title)

Maria, quae mortalium - translated separately by Bishop Bagshawe and in A Daily Hymn Book
Mary, From Thy Sacred Image - A Daily Hymn Book no. 145

Here's a novena hymn to Our Lady of Perpetual Help you may find useful.

Here is a version set to "Pleading Savior." The words are adapted from an old Catholic hymnal.

Hymn to Our Lady of Perpetual Help

Mary from Thy sacred image,
With those eyes so sadly sweet,
Mother of Perpetual Help
See us kneeling at Thy feet.
In Thine arms Thy Child Thou bearest,
Source of all Thy joy and woe;
What Thy bliss, how deep Thy sorrows,
Mother, Thou Alone canst know.

On Thy face He is not gazing,
Nor on us is turned His glance,
For His anxious look He fixes
On the Cross, and reed and lance.
To Thy hand His hands are clinging,
As a child would cling in fear;
Of that vision of the torment,
Of His passion drawing near.

And for Him Thine eyes are pleading,
While to us they look and cry,
“Sinners, see My Child, your Savior,
Who for love of you will die!”
Yes, we hear Thy words, sweet Mother
But poor sinners we are weak;
At Thy feet Thy helpless children,
Thy perpetual aid we seek.

Help us, then, when stormy passions
Sudden rise within the heart;
Quell the tempest, calm the billows,
Peace secure to us impart.
Through this life of weary exile,
Help thy children in their need;
And when death shall come to free us,
Help us, Mary, then indeed!