Measuring rear triangle alignment is easy to mess up. The string method will tell you if it's moderately to really badly out of alignment, but isn't accurate enough to actually get it back to within acceptable tolerances (the measurement isn't taken at the inside of the dropout, which is what matters). A good frame should be aligned with less than 1mm of deviation from center (again, taking the measurement from the inside of the dropouts, which determines where the wheel actually lines up w/ the frame).

If you know your wheel is precisely dished, that can at least indicate that the frame needs alignment, but a frame alignment gauge and dropout gauges are needed to correct it (center the rear triangle affects dropout parallel alignment, and vice versa, so you have to check both with each adjustment and correct accordingly). I've seen lots of mechanics screw this up however, because they forget to measure the dropout thickness and factor that in or forget to check parallel alignment of the dropouts with each other. A lot of frames with replaceable dropouts have a thicker right side dropout (most are aluminum however, which can't take a coldset); if you don't factor that in, you can misalign the frame by as much as 3-4 mm because you inadvertently align the outside of the dropout with the center line of the frame (which is what the frame gauge references from). I'd take it to a shop that can do this for you; make sure it's a good shop that won't make the above mistake, I've found it surprisingly common. If the frame can't take a coldset (IOW, is not steel), you can still have the misalignment measured and adjust the dish of the wheel accordingly; this will achieve identical results. A good shop will do all the math and measuring right, then use a set of feeler gauges to determine the exact error. HTH.