Water collected in Conch or Shankh is not usually poured on a Shivling while worshipping Shiva. Water from conch is only offered to Vishnu. As per Shiva Purana, water from conch is not offered to Shiva because he had killed the demon Shankchud. It must be noted that this rule of not pouring water from Conch on Shivling is not strictly followed.
Legend has it that father of Shankchud was demon Dambh. He was an ardent devotee of Vishnu and he had no children. He propitiated Vishnu who blessed him with Shankachud. Thus, both father and son were ardent devotees of Vishnu.
Demon Shankchud got the boon from Brahma that he will not be killed by the Trimurtis – Brahma, Vishnu or Shiva. The boon was linked to the purity and chastity of Shankchud’s wife Tulsi. The boon will be effective only till the purity and chastity of Tulsi was maintained.
The boon made Shankchud arrogant and he started harassing all living beings.
Finally, Vishnu decided to put an end to the Adharma of the demon. But Vishnu could not kill the demon as he was an ardent devotee of Him.
So Vishnu devised a plan and took the help of Shiva.
Vishnu took the form of Shankachud and violated the chastity of Tulsi. Shiva used this opportunity and killed demon Shankachud.
As Shankchud was a devotee of Vishnu, he took the form of conch. Vishnu gave him the boon that Shankh will be used for offering water to Him by human beings and Devas. As Shiva killed Shankchud, water from it is not offered on Shivling.
Note – there are numerous versions of the above story. Tulsi the wife of Shankchud became the Tulsi plant, which is considered most dear to Vishnu. The demon Shankchud is popularly known as Jalandhara. Another story has it that Tulsi cursed Vishnu to become Shaligram.