I do not believe you do, but if I'm wrong someone will correct me. I see your post has been here for a while without answer, so bump...
Getting a handle on the CC issue with shocking would be my first priority. A little CYA (20-30ppm) will make the shocking process cheaper and more effective, yes add it now.
Here's how I would begin shocking in this situation (assuming HTH CYA, as it dissolves pretty fast. Pool store CYA is reported here to be less soluble). Squish the sock after a few minutes of soaking and raise FC to shock level for around 5ppm CYA to start. In an hour or so after squishing the sock take a FC reading and up FC to CYA shock level of ~10ppm and maintain that for a few hours while you squish the sock. Repeat, repeat, repeat... Raise the FC shock level in relation to how much CYA is left in the sock after squishing all day. Once it's gone from the sock assume it's in the pool and maintain shock level for the full CYA you intended.