I'm in a similar situation (left handed and right eye dominant). I've just learned to shoot both longarms and handguns using my right hand. Of course, most firearms are built for right-handed operation, which complicates things for you if you're left eye dominant.

As a side note, it's best to learn to fire your defensive firearms using either hand. For pistols, you may need to use the other hand if your strong-side arm is injured. For rifles, when pieing a corner, it's best to have the rifle on the side that's going around the corner first.