DON!!!
I was/am in your exact position! I was a collegiate swimmer as well and to say I have flat feet is a ridiculous understatement (my feet were to wide to fit in the foot scanner at this tri store I visited in Texas!) Something I did under the direction of one of the trainers here is to start taping around the arches of my feet, until my feet, shins, and knees get stronger. Its really easy just two tight pieces of tape from the top to the bottom around the OUTSIDE of my feet and one loose piece around the inside. They told me it was important to go tight around the outside vs the inside because the small bones around the outside are the ones which are weak. Also calf raises! I do 50 in sets of 10 before and after I run and find myself doing them throughout the day. And, something you should be familiar with from swimming, is the cold tank. I went to WalMart and picked up a large enough plastic container that I could submerge both legs up to my knees (I think it was 5$). Then I stop by the gas station and pick up two bags of ice, dump the hose in with it and there's a homemade cold tank for you. I go 3 days a week for 20 minutes. You can also hit up your local grocery store for small bathroom paper dixie cups, fill them with water and put them in the freezer. After your runs rub them up and down your shins until they melt peeling the paper back as you go. I used Asics running shoes, I found them to fit my feet the best from the different brands I tried on, but each persons foot fits a different brand better or worse, so next time you buy shoes make sure you try them all on to get the best for you.
Where/what did you swim?

E

I swam at LSU and FSU. I use Asics 2140 trail shoes. They seem to work the best for me. I do the ice bath thing after a hard race, but it gets a little expensive. I ice my shins religiousley throughout the week with the ice cups. Could you explain the taping a little more?