There are two reasons that may cause dry eye. One is damage to the facial nerve, which results in the lack of tear production (which is most likely what you have). The other is damage to the trigeminal nerve, which would cause reduced cornea sensation, meaning that the cornea doesn't "sense" that it is dry so does not give the proper signals for tear production.
Lots of us here on the forum experience this problem, no matter what the type of treatment we had.
It seems that your GK treatment affected one of these nerves. Whatever the cause is, you need to make sure that you keep your cornea propertly protected and moist.
You will have to experiment and see what type of drops work best for you. Since you need to use drops very frequently the preservative free drops, in the small vials are likely more suitable. There are quite a few brands, Celluvisc that Hrissy recommended is one that many people use. I like the Tears Naturale more. The thicker ointments are also good for extreme dryness and at night (although they do blur the vision).
If your cornea is extremely irritated right now, you may need some steroid drops (available by prescription, to help ease the irritation). Some people use glasses with side shields to protect from the dry air. There is a lot of information on the forum on various techniques.
As I said, lots of us have this problem, but once you find the right regimen for yourself it can be controlled.