No problem. I've flown with handguns throughout the U.S. and to many other countries around the world. There are some universal rules you must follow within the U.S. There are additional rules you must follow for international travel, but we won't address them here, since you're flying from S.C. to Maine. Within the U.S. you MUST:
1.) Carry your unloaded handgun in a hard, lockable case. You may have to unlock the case for TSA to inspect the gun, after which it must be re-locked by you or TSA personnel.
2.) Declare the gun at the airline counter, and declare that it is unloaded, signing the appropriate form, to be put INSIDE the case.
3.) Carry your ammo "in an original factory container" in a SEPARATE piece of lockable hard luggage from the handgun. I have never had a problem carrying ammo in an MTM style plastic case, through dozens of inspections in dozens of airports in the U.S. and abroad. If you're concerned, transfer your ammo to some factory ".454" labeled package or container.
These inspections take a bit of time. Arrive at the airport early, and allow enough time between transfers that laggardly baggage handling will still allow your guns and ammo to make it. I'm guessing that you'll fly from Charleston to Charlotte for a transfer, with another transfer somewhere in New England. Try to avoid NYC.
I would definitely advise you not to ship your guns ahead.
