There are 7-speed STI shifters, but they may be hard to find. Some options:
1) Buy 7-speed STI and keep a 6-speed cassette/freewheel; it may work to try Sheldon Brown's alternate cable routing:
http://www.sheldonbrown.com/derailer...html#alternate
2) Change out your 6-speed for a higher-number of gears and buy a matching set of shifters.
#2 gets a bit complicated. Do you have a freewheel or cassette?
http://sheldonbrown.com/free-k7.html
If it's a freewheel, you may be able to just thread on a 7-speed freewheel; you may need to move spacers over from the non-drive side to the drive side and re-dish the wheel. To move above 7-speed, you'll need to change out the hub for one with a free-hub that takes cassettes.
If it's a cassette currently, the freehub body will likely be too short for anything above 6-speed. You may be able to change out the freehub body for a longer one, adjust spacers, and re-dish. But it may just be simpler to eplace the hub or whole wheel.
Going above 7-speed assumes you have a steel frame. 6- and 7-speed typically use a 126mm dropout width, whereas 8-speed and up use 130mm. Steel frames can stretch; aluminum can't.
Lastly, since you have a double crank, you can use a double or triple front shifter.