My LG is def teething- her symptoms include constantly chewing on something (hands, feet, rattles etc), drooling aaalllllllllll the time, folding lips in, a little fussier than usual. She doesn't seem congested but I'm fighting something. Definitely do not leave baby in the car seat for a long time. The AAP says 2 hours max! I'm gonna be honest, if she is acting like she's in pain I give a little infant tylenol and that helps but I try hard to do other things first!
I'm pretty sure that mine is teething because he's become super drooly, always chewing on something, fussier than usual, harder time falling asleep. But not cool that your doctor dismissed you! You know your baby and know if it's different. But they likely wouldn't do much for a cold anyway. I say you trust your gut and do what you can for your little guy's cold symptoms. Don't leave him to sleep in a car seat, though, that's terrible advice!
I'm fairly confident that my daughter is teething. She's very fussy, crying a lot more than usual, won't sleep unless outside or on top of me, she's on and off the boob constantly when trying to eat (ouch), chewing on anything near her mouth, drooling constantly, and wants to be held constantly while she is usually fine with being independent. We did have colds a few weeks ago and she does seem congensted still but this feels different and I believe I saw signs of a tooth this morning but she wouldn't let me check. My son was like this for months before a tooth popped in. No don't just leave your little one in a car seat to sleep. Try sitting in the bathroom with the hot shower running for a bit to help with the congestion. I think the doctor should have checked but I also don't think they would do much unless your little one is dehydrated, at least where I am.