There have been countless threads on this in the past, you can always look them up for more suggestions in addition to the ones you get here.
My baby (now 14 months) was a terrible car screamer. It was truly, truly awful and I felt as traumatized as he was!
Luckily, I do not rely on a car, and we used (and still use) public transportation as much as possible, But we drive places together as a family a lot. So, that means I could get in the back seat while DH drove. I was able to nurse the baby, while sitting in the middle seat (with seat belt on!). It was not comfortable and probably not totally safe, but it worked. And I nursed him every.single. car ride!
The magic bullet for us was when he outgrew the bucket seat (BTW we were able to use a convertible seat on vacation and it made no difference) and we got the forward facing bigger, more upright seat. Bam! No more crying! I think he just hated facing backwards. Maybe it made him naseous, or he just felt left out, who knows.
I know some mamas keep their babies rear-facing as long as possible, but quite frankly I was eager to get him FF as I suspected it would help, and it sure did! Besides, the country where I live (in Europe) all the car seats for babies over 9-12 months are forward facing anyway so I actually had no choice in the matter.
I know this doesn't help you, if you can't get back there to nurse him as someone else drives and none of the other tips work for you as was the case for us, you may have to just white-knuckle it until you can get your babe forward facing. I know how horrible it is. Hang in there!