1. Ice massage directly to the area of muscle and bone. Otherwise, general ice if you can't ice massage directly.
2. Massage along the area of pain + muscles. Basically aiming to increase blood flow to the area to help it improve quicker.
3. REST if you can. Overuse is generally the main cause of shin splints (looks like the case for the OP as well) so rest should theoretically clear them up. But it's important to add in other recovery protocol.
4. Light strengthening work for your tibialis anterior (fill a backpack with some books and sit on a counter and put it on your toes and move it up and down) + stretch out your calves.
If it's overuse of the tib anterior from heel-toe running work the eccentric motion (negative portion) of the backpack toe exercise especially.
4. Wraps CAN help mitigate the symptoms, BUT they will not solve the problem. If you need to keep on performing for a sport or whatever, then it's fine. Otherwise, avoid them.
Same with orthotics/insoles/shoe stuff. Fix the problem, don't try to mask it... more on this in the next section.
5. IF you're a heel-toe runner, this can cause shin splints problems because all of the stress goes directly to your joints and bones INSTEAD of being absorbed by your muscles. Learn to run PROPERLY with POSE or CHI running (can google both these methods).
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For flat feet:
1. Strengthen your gluteus medius. Clams, hip hikes, single leg balancing keeping the hips level, etc.
Improperly firing or inactive gluteus medius means your opposite hip dips while you're walking, which leads to valgus stress (and thus deformation of the knees -- aka knees cave inwards). This also leads towards pronation of the feet leading to flatness.
2. loosen up the muscles in your hips/thighs/legs with massage (myofascial & cross friction) as well as with a foam roller and/or tennis ball.
3. Strengthen the muscles on the bottom of your foot to help "reform" the arch. Toe flexion/extension exercise such as picking up things with your toes and then putting them into a box are fine. Walking on sand... etc.
4. Shoes in general suck. Walk more barefoot.
Also,
http://www.biggerfasterstronger.com/uploads2/08_JanFeb_FlatFeet.pdf
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Frankly, a lot of advice in this thread is crappy,... no offense to anyone. Just cause you've had shin splints before and they went away doesn't mean you know how to properly treat them.
As always, this is the Internet so you would be wise to fact check any material anyone here including myself is putting forth.