I'm training for my 1st marathon and I think have a classic shin splint injury, what's the best course of action?

Eval by Sports MD. If you are training for the big apple event you have precious little time. You should be seen expeditiously by an orthopaedic surgeon who handles runners' injuries regularly. A true stress fracture needs to be ruled out via xray and/or mri. Aggressive nonoperative management on your timeline may mean a cam walker/boot for a week for real impact stress releif, new running shoes, nsaids, etc.
Could be... Shin pain (aka "shin splint") may come from medial tibial stress syndrome (mtss), stress fractures, or compartment syndrome. Identifying the underlying reason for your pain can then help with a specific plan of care. Treatments usually consist of rest, stretching, ice, massage, or orthotics. (drmarkgalland.Com) you may need to plan on cross-training.