The short answer to this question is, “yes”. You should try and make sure that you see a doctor after an auto crash as soon as reasonably possible, ideally within a day or two of your accident. The adrenaline from an accident can lead to overlooking your injuries, and the impact from even a relatively minor accident can result in injuries that you may not be aware of at the time.
Because you may not have the opportunity to properly brace yourself for the impact from a collision, your body may suffer from whiplash or other kinds of damage even if the accident did not result in significant damage to your car.  It is important to your recovery that you address these as soon as possible before they can be unknowingly worsened through time or other activities.
Insurance companies are very likely to check to see if you promptly sought out medical attention after an accident. Failure to promptly seek medical attention after an accident can make negotiating with insurance more difficult, and can damage your claim if you eventually decide to take it to court if the other party claims that your injuries were not from the accident and may have come from somewhere else.