I am experiencing the same exact thing as OP, new to fixed riding, skidded like a madman, then great leg soreness, especially when lifting leg up...
90% of the pain is in my dominant right leg. will try stretching and skid more progressively. while researching cycling pain problems, most solutions seemed to indicate proper bike fit, mainly saddle height. mine is pretty slammed down, could this have to do with this, or is skid leg soreness a whole different issue ?? i've never really experienced discomfort while riding fixed before trying to skid..