Hi... Don't be scared of fixing a grounding issue, which is almost certainly what you have. The classic sign of this problem is it showing up when you aren't in contact with the strings, because when you are in contact with the strings you become the ground. The noise appears when you are not the ground, because there is no ground.It's a simple fix, if you aren't up to the soldering job then it won't be hard or expensive should you need to find a repair person.
Provided that this isn't the problem, then you would probably want to consider upgrading the shielding on your guitar. You don't say what kind of guitar it is, though, so I'm assuming a single coil. Shielding isn't much of an issue on humbucker equipped guitars
