I have a CDL permit and I have a CDL driver with me in the vehicle. Do I have to have a medical card in my possession?

Yes, if you are traveling in intrastate commerce.  If you are traveling in interstate commerce, you should have self certified yourself as Category 1 (non-excepted interstate) and provided a copy of your medical card to your states driver’s license division.  Your medical status would then be available on your CDLIS (Commercial Drivers License Information System) record.