I'd personally just go for new shoes and see if that fixes anything. I'm bad at tracking shoe mileage/getting new shoes before my old ones are trash. Though, when I start getting any kind of shin/foot/ankle type injury and I know my shoes are at the end of their life I will immediately get a new pair and... wua-lah, pain is gone!
Otherwise just see how that down week feels, it might give your legs/shins some rest and you'll be all good after that.
I'd also continue with the icing just to be safe. I also found that toe raises work fantastic for me. Stand with your heels on the edge of a step with the rest of the foot hanging off the step. Raise the toes up and down a shit ton, relatively slowly. Shins should be burning. Do this multiple times a day.