Suing my employer

I work for a hospital as an accountant. I took my one year old daughter to be treated at this hospital and she was in and out admitted for several months. After not being able to find a diagnosis and being dismissed on multiple occasions from this hospital, I went to get a second opinion out of state where they repeated imagines and found a malignant, aggressive tumor in my daughters chest.

After requesting my employers hospital to review their images, it was found that they missed this diagnosis.

The timeline for her diagnosis could mean life or death. Had we found this sooner, her treatment would have been different with a better outcome.

Do you think I would be able to sue my employer for the care my daughter received and still keep my job?