The easy answer is no, that is not an overreaction to the problem as you've assessed it. You didn't want to drive to begin with, because of doubts about your capacity to drive, then when you did drive you encountered a dangerous situation and now you don't to do it again, that's just rational.
The tricky part is deciding if you're going to persevere anyway. Though not wanting to drive again is rational and probably good for everyone else on the roads, you are also most likely not uniquely incompetent even if you're self critical and doubting. This might be where the idea that you are overreacting comes from, the tension behind this rational response and the simultaneous idea that perhaps you're being too self critical. Ironically, I think both are true.
For better or for worse we're living in a world where you can continue to do this and on balance of probabilities, you will get used to driving and get more capable with it, but there'll be a period while you reach that stage where you and everyone else on the road will be at risk of harm. That's not a great situation and something that in other contexts for other activities might not be tolerated, but it also might be a necessary one. It might perhaps put your mind at ease (or the opposite depending on how you interpret this), to realise that the road is full of drivers that might not be "good" drivers because they're, nervous, have bad multitasking, are drunk or on drugs, are tired, aren't concentrating, are underconfident, are overconfident, angry right this second, inexperienced, over experienced to the point of becoming inattentive and all manner of factors that should objectively mean people just shouldn't drive but nevertheless we do and in the time and circumstances that we find ourselves in you wouldn't be against the moral zeitgeist on this to decide that driving is necessary or beneficial enough for you that you're going to become just one more such driver less than optimal driver in the roads. Hopefully after a while you'll get past the fear and inexperience and that will make you a driver of at least average competence.
This isn't to say I think you should do that. One less car on the road, especially driven by someone who by their own judgement thinks they aren't a good driver and also doesn't want to drive would, in the grand scheme of things be good, but I acknowledge it would be hypocrisy of me to suggest that you should exclude yourself on this basis when very few of the rest of us would.
I was unbothered by it as well, at least intestinally, the physical pain of something hot enough was certainly something I could experience and dislike at the extreme end but my stomach and bowels would have been fine. That it until about the past 5 years or so when my stomach suddenly decided it couldn't handle all kind of things that were never a problem before and now I totally get what people were talking about. It's pretty sad, I miss being able to reliably tolerate highly spicy food.