You are responsible for proving that you were injured as a result of the accident.
It is a commonly held belief that if you aren’t hurt badly enough to seek immediate medical attention, then you weren’t hurt that bad and the settlement offer will reflect that belief.
The longer you delay treatment, the less believable your complaints of injury will be viewed. “Because after all if you were really injured, you would have seen a doctor right away.” Whiplash, for example, does not always show up immediately, but it should within days.
The bottom line is you should see the doctor as soon as possible. You don’t want the adjuster or the insurance attorney arguing that you couldn’t have been hurt too badly, because after all you didn’t even bother to see a doctor for two weeks.