Is it ok to get liver mri with contrast done done when you have common cold symptoms (little cough, runny nose etc)?

Depends on what: The answer depends on what the liver MRI is meant to detect. You have to weigh the risks & benefits of ALL scans with the severity of the illness you are attempting to diagnose. I doubt the MRI is meant to help you with cold symptoms. Consider that MRI contrast DEPOSITS IN YOUR BRAIN for the rest of your life after inject & its long-term effects are unknown. If you have liver cancer, that's worse.