Would a sinus MRI scan also show nasal bones and cartilage?

yes is the simple answer. However the skill is in interpreting the scans. You need an experienced radiologist and surgeon working together to appreciate the relevance of the scans to the symptoms and treatment.  

Thank you for your query.

MRI scans are good for soft tissues, whilst CT scans are good for bone. If you wanted to look at your nasal bones, then having a CT scan would be more appropriate. Also make sure you have a good radiologist would can correctly report the scans for you.

Kind regards,

Thank you very much for your question.

As a "rule of thumb" the MRI is the first choice to study the soft tissues while X-ray or CT scan are indicated to visualise details of bone and cartilage. The latter is the most accurate method to study the paranasal sinuses.

Nevertheless I would recommend to discuss your concerns with a board certified plastic surgeon with specialist interest in noses rather than "refer yourself" for complex imaging. He will certainly be able to guide you through the correct diagnosis and suggest appropriate treatment.

With kind regards,