You can side sleep immediately after breast augmentation. The idea is to not allow your implants to move from the dissected breast pocket until the pockets have scarred down (creation of a capsule).
This occurs by 4 weeks following surgery. Regardless, as long as you wear a breast band (my favorite is the Mermaid band), you should have no problems with any activities that don’t require heavy weight lifting with your arms. The only exception is sleeping on your tummy in the early postoperative period which can push the implants out of their pocket.