Could they have been like the Ring and had a “life” of their own?
There is no evidence that the Silmarils were like the Ring or were in any way aware or that they had a built-in master. But this was not needed.
Feanor made the Silmarils using, in part, light from the Two Trees which were the most sacred things in Valinor. And after he made them,
...Varda hallowed the Silmarils, so that thereafter no mortal flesh, nor hands unclean, nor anything of evil will might touch them, but it was scorched and withered;
This happens not through the will of the Silmarils, but as a consequence of the blessings Varda put on them. So when Morgoth stole them, even though he did not touch them directly:
In his right hand Morgoth held close the Silmarils, and though they were locked in a crystal casket, they had begun to burn him, and his hand was clenched in pain;
It didn't go well for Morgoth:
His hands were burned black by the touch of those hallowed jewels, and black they remained ever after; nor was he ever free from the pain of the burning, and the anger of the pain.
For a creature of evil, the Silmarils might as well have been made of red-hot iron.