Could squamous cell go into the cartilage of my nose or is it just in the layers of the skin?

Thanks for your question. 
Squamous cell cancer typically starts in the layers of the skin, but as it progresses can start to involve deeper layers and structures including cartilage.
It is important to have suspicious lesions evaluated and if positive for squamous cell cancer, promptly treated. 
Best of Luck

Nasal cartilage can be damaged by squamous cell carcinoma, however, even if it is not directly involved with the tumor it may still have to be sacrificed because of the complex structure of the nose and the proximity of the tumor. The major benefit of Mohs surgery is that it has the highest cure rate of any other treatment, which means the lowest chance of recurrence. Discuss this with your Mohs surgeon as well as reconstruction options once the tumor is removed that will restore normal function and appearance. Do this before your surgery so you can have a clearer picture of what may lie ahead for you. Since there are Facial Plastic Surgeons who possess special expertise in nasal reconstruction, you can discuss this with your Mohs surgeon to see if one is available near by. Fellowship - trained Mohs surgeons may also have the ability to deliver similar results.