The most effective medication for myotonia congenita seems to be mexiletine or Mexitil. It is used to treat heart arrhythmias but since it's a sodium channel blocker, it improves the chloride conductance in myotonia.
The normal dose is 200 mg 3x a day. However some young men in sports just use it as needed and don't have a set daily dosing schedule. You would have to ask your doctor about that. You need to get an EKG and be monitored to be sure it isn't affecting your heart. Most people tolerate it well, but some have fairly serious side effects. It's best to start with a lower dose and work up gradually.
There are other medications but they tend to be less effective or have greater potential for side effects. They would be Diamox, Dilantin, Tegretol, Lamictal, and Quinine Sulfate.