Your ears shouldn't be popping during a cold. It's usually a good thing as it prevents viruses/bacteria from going into the ear through the Eustachian tubes. Trying to crack the ears too much isn't good for the eardrums and may cause Eustachian tube inflammation. I would avoid getting any medicine in the middle ear that's not intended to be there. Flonase in the ear is a big no no. I think on the flonase package it says to point it at an angle so it doesn't go in the nose that much.
You can always go to a doctor or buy one of those otoscopes and have someone look into the ear for signs of fluid/redness for a middle ear infection. As for inner ear infection just look out for symptoms of vertigo, fullness, etc. Basically report any symptoms to your doctor.