Kirby - where do you store your rifle? If it's that humid you may want to buy a dehumidifier. If you keep your rifle in a gun safe you may want to do what I did. I ran an elec. cord into the safe and installed a porceline light base. I keep a 40 watt bulb burning in the safe and it keeps the temp in the safe above the room temp which forces the moisture out of the safe.
Do not store your rifle in a zippered gun case (soft case). These things draw moisture like a sponge.
I've never had any trouble with guns rusting. I treat my bores with Montana Xtreme Bore Conditioner and wipe the outsides down with regular 3in1 oil. (I also use 3in1 to lightly lubricate the locks on my sidelocks.)