If you do not have significant pre-existing conditions and the impact is relatively minor, it should be okay to go directly home after cooperating with the police investigation of the accident.   Follow up with medical treatment if/when you feel symptoms. 

It is not uncommon for shock and adrenaline to mask our pain immediately after an accident.  Our instincts tell us that we'd much prefer to be in the comforts of home than subject ourselves to the further trauma of an ambulance ride or a visit to the emergency room.  Under these circumstances, take your time and exercise prudent judgment.  Police officers and/or paramedics will normally ask you if you desire medical treatment.  They also may give you advice based on their experience and observations of the circusmtances surrounding the incident.  If emergency personnel recommends that you get immediate medical care, trust their experience and judgment.