Burnt rubber smell

It could be but normally the gaskets are not large enough to smell if they are "melting." Plus this gasket is a hard plastic which again, will not put off a smell strong enough to smell that quickly inside the vehicle.

I suspect you have something rubbing a tire. Do you hear any noises when driving? I would suggest starting with checking each tire all around both inside and outside edges to see if there is any wear. A tire would make much more sense based on how quickly and the strength of the smell you are experiencing.

You may also want to inspect the valve cover gasket for a leak which could be leaking into the exhaust or inspect the entire exhaust system for a plastic bag that has melted on the exhaust system causing the smell.