Honestly, we went through this for several months, but because the infant seat (ours was a SnugRide) was safer when she was so small, we waited to switch her to our Britax until recently.
Things I found helpful when baby was miserable in the car: Rescue Remedy before we went anywhere, and a full tummy/nursing prior to leaving in the car. Also having a toy that lit up or made some sound was a helpful distraction -- thing is, I pretty much hate those kind of toys, but we were pretty desperate, and one toy like that helped if it wasn't too obnoxious.
I personally think some babies are just overwhlemed by the car: noises, vibration, bright light, etc. And so having anything you can to help make it not so overstimulating is good (like shades on the windows, etc.). Obviuosly if it's overstimulation in your baby's case, a very bright light-up or noisy toy would not help.
We got a little stuffed bug from Target (said surface wash only but it was fine in a pillowcase) that would light up and play music, and had a hook thing to latch it to her carseat. That way when everything else failed, it would sometimes work to focus her attention so she could relax. The Gloworm also helped.
And try singing! Singing helped us a lot too.
And when in doubt, find a safe spot to pull over and nurse. (I love church parking lots for this.
Even though the Britax might fit your child well enough at this age, try putting baby in it before you install it, and make sure it's reclined in the infant position to check the fit so she's secure. Ours was just too big for our baby when she was 11 weeks old. Yours may fit fine! But we found over time, taking some shorter trips in the car just to get her used to the sound, etc., was helpful. (I'm talking drive around the block a few times.) You can also try sitting in the car with it running (not in a garage obviously) and nurse her, so she can start to associate the car with a calmer activity? Then after nursing, put her in the carseat. Or just take her back in the house. But have the car running while you're nursing so she'll hear the sound, etc.?
I think it's an association thing sometimes with some babies, so trying to find a better association might help.
And in our case, she just eventually grew out of her car-hatred. But I'm convinced it had less to do with the seat and more to do with the experience (though that might not be your case -- and we were very careful about adjusting the seat and straps so it was safe and snug but not uncomfortable -- our baby gets hot easily and that was one big factor this summer). And honestly, during the worst of it, I found myself staying home and not taking her out if I absolutely didn't have to. It was better on us both that way.
Yours will grow out of it eventually! But try some of those tricks and if it still doesn't work, then switch seats (just be sure to keep it rear-facing).
GL!! And you're certainly not alone. And I'm sorry you and your wee one are having a hard time. It does suck.