I'm w2d2, too! I've used this program (seasonally) a few times.
For muscle soreness, I swear by hydrating and having a protein shake (or a meal with plenty of different kinds of proteins) afterwards. Gentle stretching might feel good, but it's never helped the soreness go away for me.
For shin splints, I use compression and ice afterwards. If it is really bad and I can't sleep, I'll take ibuprofen, but I try to avoid doing that.
I find that these things help prevent me from feeling bad soreness during my next run so I can do my best.
If it gets bad during a run, try taking smaller strides or walking if necessary. Do what you can, but never overdo it when your body hurts; otherwise, it's harder to recover.