Certainly, you should visit an orthopedic surgeon and get an X-ray to find the underlying etiology for shin pain. However, for symptom relief, here is what I'd do:
Keep the legs elevated.
Use ice packs to reduce swelling. Shop for cold compresses.
Take an over-the-counter anti-inflammatory, such as ibuprofen (Advil) or naproxen sodium (Aleve). Shop for ibuprofen and naproxen sodium.
Wear elastic compression bandages. Shop for elastic compression bandages.
Use a foam roller to massage your shins. Shop for foam rollers.