Poor Izzy!!!
I'm sure she is fine, bullies are VERY tough puppies. Tilly bangs her head on absolutely everything - it really used to freak me out, she NEVER cries out in pain for anything, and she is always fine.
Just ask your vet to double check her next time you go (she's the same age as my bully, and we practically live at the vet for all the vaccines they get!).
As for car safety, I have this for my baby (as well as the matching harness):
http://www.petco.com/product/112434/Petco-Premium-Seat-Belt-Harness.aspx?CoreCat=OnSiteSearch
http://www.petco.com/product/112437/Petco-Premium-Dog-Seat-Belt-Extension.aspx?CoreCat=OnSiteSearch
It has been WONDERFUL. Matilda used to sit in my lap, but she got VERY squirmy and VERY big VERY quickly - it just wasn't safe for either of us. The passenger side was awful as well, because she's pull on my E Brake and I just couldn't stop worrying about what would happen if we got into an accident - she'd go straight through the windshield. And letting her just in the back wasn't good either. I'd check back there every 4 seconds because I was so worried about what she was doing. Finally, one day I heard a yelp and just about wrecked the car when I turned around... Tilly got STUCK, butt-up in between the front and back seat! It was hilarious but awful. She was like a little wedged sausage.
Thus, I bought the seatbelt. I tried just the harness portion, and while it was effective in safety, Matilda got tangled super easily, since it latches them to the seatbelt with no breathing room. At one point, one of her hind legs was stuck in the air! So, MAKE SURE you buy the extension. Even if you choose just to use a regular harness and not the padded one, the extension is the best.
Now, she is able to sit/lay comfortably in the back, look out the window, and if I stop short, open the doors, etc., I know she is perfectly strapped in and safe. I mean really, you wouldn't toss an infant in the backseat and hope for the best, and you shouldn't do it to your puppy for the exact same reason.