I would say it could very well be the difference in temperature that is affecting the pressure, but honestly I can't say I've had that happen or had the need to put an icepack on my head, back yes, head no. You could start by asking a pharmacist if this is a common thing, I'm sure they see a lot of things or are familiar with a lot of these types of things. Saves you an immediate doctor visit. But if it persisted I would definitely bring it up with my doctor asap. If you think it's spinal and not simply ear popping then right away.
swelling and pressure will go down with cold. your Eustachian tube, (which connect your ears to your sinuses, are probably popping. i dont think it can cause any damage. the head ache is probably from tension in your neck. try ibuprofen to help with the swelling, vs Tylenol for your head aches. sorry u hurt, but you shouldnt worry too much about the poping