If i had an mri with contrast would that detect and cancerous lymph nodes that are swollen in neck?

Yup: If the MRI was of your neck it would detect masses/abnormalities of that kind to a certain size.

Very young for cancer: At your age the lymph nodes in your neck are probably due to a reaction to infection or other inflammation. It is unlikely that they are due to cancer; however, MRI can often detect abnormally enlarged or abnormally shaped lymph nodes.