Is it OK to use cryotherapy after having CoolSculpting done? I use it as recovery from sports injuries/workouts/etc.

No problem!  You can use standard cryotherapy after CoolSculpting.  With little to no downtime, most CoolSculpting clients can return to their normal daily routines right after a treatment.  That means work, play, exercise and recover, or whatever it is you do.  If your recovery routine includes cryotherapy, including whole body cryotherapy, that will not augment your CoolSculpting results or the ability of your body to complete the cryolipolysis process.  
Thank you for your question and best of luck with your CoolSculpting results!  
For those not familiar with cryotherapy: basic or standard cryotherapy for post workout recovery and injury treatment include ice packs, ice water baths/ cold water immersion, cold gel packs, and ice massage.  There are countless other cryotherapy devices available on the market.  Always consult a reputable advisor or physician before purchasing or using one of those products.