The immediate fix is to cut running almost entirely for 2-3 weeks, then rebuild slowly using the 10% rule - never jump your weekly mileage by more than 10%. I made the same mistake a couple years back, went from 20 miles to 35 in like 6 weeks, and ignored the warning signs. By the time my shins were actually painful, I'd done enough damage that I couldn't run for nearly 2 months. Cross-training like cycling or swimming keeps your aerobic fitness up without pounding your shins, and honestly that's what saves your sanity during recovery.
The ice and stretching thing does help with inflammation, but it's not a substitute for backing off the volume. Ice after any activity you do, hit your calves and shins with some massage work, and throw in calf raises or eccentric heel drops a few times a week once the acute pain starts fading. But here's the thing - your tissues need actual time to adapt. Collagen remodeling isn't fast, so even if the pain goes away after a few days, the structure underneath is still fragile. Come back too soon and you'll re-injure it.
Give yourself a real break first, then spend the next 8-12 weeks building back up properly. It sucks way less than dealing with chronic shin splints for months because you tried to push through too early.