Not had it with bicycle offs particularly, although being sideswiped/left hooked in a cycle lane has made me more vigilant for cars that might do that next time, I consider that sensible rather than anything else though.
I did get that fear after my motorbike accident. I think it was because it was sudden and arbitrary. There was little I would do differently a second time, maybe a bit more vigilance but it would have been unlikely to stop the incident happening. I was a basket case in a car for the week or two following the accident. Also hypersensitive of the other vehicles around us and positive that every one was going to hit us. It took me that long to be comfortable to drive again. First time out on a motorbike, taking my wife's for an MoT, was very similar. I was careful, ultra careful, with speed, road positioning, observation and again positive that every other vehicle on the road was going to drive in to me. I didn't replace my motorbike for 2 years, pretty much the length of the insurance claim, I think mentally I had to have it all finished before I could move on. But I missed being on a motorbike and eventually that want to still do it, coupled with two years of incident free car driving, meant my perception of the road had changed back to something more akin to how it was before the accident.
So, it can go away. It works differently for different people and a chunk of it probably depends on your motivation. Commuting to work regularly by bicycle I've found getting back on is easier because it's an expected part of my life. It's definitely about the lack of control, about the fact that they did this to you. So expect to be more sensitive to other vehicles and probably, as others have said, more caustic and shouty around them, at least until you realise they aren't quite all nobbers.