There is quite a lot of stuff on the internet about car seats and flying. Most of it is American, so if you have a look at that, it might help you with regards to the 'special label'. We've never flown to the US, only within Europe / Cyprus, so can't help with specific US regulations.
I think in general the staff at the airport / on the plane seem to be less strict than the ones 'on the phone'. We've often been told no to things, only for somebody at the airport to say it is fine.
One consideration, if they say at the airport that you can't take your car seat on the plane, would you be happy for it to go in the hold? I didn't want my isofix one going in the hold and possibly getting knocked, so we got a cheaper one to take on the flight.
You can get grobags which are designed to fit in carseats.
Remember to bag your buggy up well, or it will get knocked and scraped - we've used either a stoller bag / surf board bag / heavy duty garden rubbish bags and black tape. Good to have extra on hand to put car seat in if needs be.
Medised sounds a fantastic idea, would probably have used it if we had flown for any longer distances.
Can you ring the Continental desk at the airport and see what they say?
Hope you get it all sorted.