well ok a cig socket the ones u ind in your cars are all rated to 10 amps the cig plug that are on most items are rated to about 8 amps max, if its blowing then there is 90% a short circuit in the plug its self, thats why the fuse blows instead of your wiring going all ape shit on you, i would never recommend you replace the 10amp fuse n the socket with a 20 amp fuse if you do then u will have a wiring harness in ya libs going ape shit on you.......
i would either try another device to check if the socket is faulty, if the socket is fine then the plug that is plugging in to it, u can get a new plug from
jaycar check this link and re wireing the plug to elimate the short.....
oh yer dont worry i have customers that come to me on a regular basis with the same therory of upgrading the fuses to bigger ones...