Thank you all for the suggestions! He's still fairly new to our family. We got him in June, and he's become super attached, so anxiety might be the case. The funny thing about it is the fact that when I bought him, we drove a little over an hour to get him. On that long drive home--he laid on my lap the whole way--he never even acted sick at all. Now, we can't even put him in the car without him getting sick.
I've never had a dog before in my life, so all my worries are amplified with Smokey. He's my only baby, and I want to make sure I do everything right.