Nose is burning inside, what could this be?

Oh poor you, this must be so uncomfortable, but yes it does sound like its related to your recent cold.

You could ask your doctor for medication, or try a simple home remedy = make up a warm saline solution, using sea salt, and sniff it up the nostril to rinse out the area, its very soothing to do this, I have used it myself.

I hope you get better really soon.

All the best x