What can I do to speed up my case?

The one, and only way to do this is to go to the doctor.  There is no other way.  Remember, (unless you were dismembered, disfigured, or paralyzed) you do not have a "case" to settle until after your doctor has formally discharged you from all medical care with a medical finding that you suffered a particular kind of permanent injury that will qualify you to be paid for your injuries under a special Florida law.  This medical discharge occurs only when your doctor (not you, your relatives or even your lawyer) determines that your injuries from the accident finally stop healing (usually about six to eight months after you begin treatment).  You cannot speed up the time for settlement if you voluntarily quit going to your doctor on your own.  (That would actually destroy your case, and is not a "doctor's medical discharge".)  Generally, the sooner your doctor discharges you from medical care, the less money you will receive  (because that makes it look like you were not really hurt).  So, do not try to rush it.  Generally, the longer your doctor takes to discharge you from medical care, the more money you will receive (because that makes it look like you were really hurt).  So, take your time.