M.M.
We traveled with my son when he was 2 to NYC also. At the last minute I bought a travel car seat. It was like putting on a backpack on him and then using the car seat belt to attach it to the cab. But it was so new to my son and with the new experience, he through a huge fit and we couldn't even keep it on him. So, I just held him in my lap. The traffic from the airport was so slow that it seemed to be okay. Most people don't use car seats in the cab, which I learned when I was there. Good luck! I also H. your doctor's appointment goes well.
-M.