My own inclination, in the case of a minor injury, is to ask for coverage of actual expenses, including costs such as time lost from work, transportation for medical care, any child care needed as a result of the accident, and take-out meals if I couldn't cook for awhile. (I presume you kept receipts, mileage, etc.) More than that pushes a claim into an ethical grey area that might be described as, "Well, other people get generous settlements for pain and inconvenience, and I should, too."
What's wrong with that thinking? Several things.
1. For the most part, people who hire lawyers get bigger settlements than actual costs. The lawyers get rich, the insurance companies raise their insurance premiums, thus increasing their profit margins. The injured may get richer. But the average consumer gets the bill.
2. Other people getting big settlements tend to give everyone a greater feeling of entitlement. That doesn't make it right, and we help perpetuate a system that doesn't really work optimally for most of us. If you had an angel sitting on your shoulder, what do you think you'd tell him is a reasonable amount for what you actually suffered? (Ask the insurance company for that amount.)
3. Life is risk. No getting around it. Modern life, with lots of auto travel, increases risk (including the inconvenience we suffer when something does go wrong), which is something we must balance against the increased convenience of driving cars.
4. They're called "accidents," and not "plans." Next time, you could be the one at fault – it only takes a moment of inattention, or even a sudden, confused situation where something HAS to go wrong. Imagine how you would feel if someone were trying to stick it to you for a big settlement on a relatively small injury. (My first husband actually did this. In his case, it was clearly fraudulent, and if I hadn't been intimidated by his temper, I would have opposed his choice vigorously.)
5. If you were injured by someone behaving in a rude and reckless manner, then a punitive settlement might be warranted. But really, the legal point of that is about correcting the other driver, not making you wealthy.
There may be folks who suggest you go for all you can get, in which case you should hire a lawyer. But you might not be happy with the struggle that could initiate. I had a car back into mine in a parking lot a few years ago. It jolted me pretty hard, and I suppose I could have claimed an injury (though I didn't even get bruised.) I found that by simply being polite and letting the other insurer take the lead, I got a quick and easy settlement for my actual expenses with no hassle, and never lost sleep over the process. If I had grabbed for more, I might have bought myself a long, hair-tearing fight. And might not feel so comfortable with my conscience now.