Uh huh...I've been lawn darted and landed on that part of the back before. Took about 2weeks before I could walk w/o pain another few weeks to finish healing.
Typically with an injury the 3rd day post injury will be the day of the most swelling and pain. If however you find that it continues to swell or becomes more painful you MUST go to the doctor.
You also need to go to the doctor if you feel dizzy, nauseous, have numbness in your leg etc., etc...
In about a month's time I suggest you visit a chiropractor to make sure everything is lined up correctly.
You might also consider wearing a vest from now on...which would have helped protect that area. I ride with a vest quite often now...always when jumping or hacking and sometimes when doing flatwork depending on the horse.