You say that you've iced like crazy, but I wonder if you've iced in the way that I first iced as a 19-year old, and that I continue to ice after every run. Longtime posters here have seen me give this advice a few times, always when somebody complains of shin splints.
Assuming that your trouble really IS shin splints, rather than a medial tibial stress fracture (which I've had, too) or medial tibial tendonitis, here's the protocol.
Immediately after your run, pull on a mid-calf athletic sock and fill the medial portion--over the sore area and beyond--with crushed ice. (I have a nylon bag that I fill with a tray of ice cubes, then bang against the floor to break it up.) Roughly crushed is okay. The ice should be directly against your skin. That is crucial
Leave the ice in place for 10-15 minutes. I used to leave it for a full 20 minutes; now I leave it for 10 minutes. It will numb out in about five minutes. Just leave it there. Then slide off the sock, still full of ice, and empty the ice into the sink.
That's it. Do it for a week. You can continue to jog short distances during that week, or jog on alternate days, or just take the week off. If you have shin splints, your pain will be notably diminished.
This cure will also help medial tibial tendonitis. In that case, make sure the extends all the way to the little bump--the attachment point just below and ahead of your ankle.
This cure will NOT work on a medial tibial stress fracture. That will require at least 10 weeks of zero running, and maybe more.
Have you thought about just giving up running for six months and switching to cycling? Some chronic injuries respond to that. Some don't--achilles tendinosis, for example, which will just sit there unhealed. High hamstring tendinopathy, in my experience, also requires ART or other PT interventions. (I'm speaking from personal experience with all these injuries, not as a healing-arts practitioner.)
But shin splints: crushed ice on skin for at least 10 minutes immediately after the run. Also: don't jump into a hot shower immediately after taking out the ice! Your shins will scream if you do that. Give the cold a chance to dissipate. Or shower first, then ice.
Good luck!