Whether or not spin will help or hinder your distance depends on what your swing speed is. Higher swing speeds benefit from less spin, and lower swing speeds benefit from more spin (the spin helps the ball stay in the air).

Other issues that could be contributing to a lack of distance: attack angle, ball position, impact location, and loft.

If you have a negative angle of attack (hitting down on the ball) then you will create more spin. A positive/upward angle of attack will create less spin.

Teeing the ball higher may help depending on how you currently tee it, but you obviously don't want to tee it too high. I like to use the creases of my index finger to help me maintain a consistent tee height.

Also, ball position could be an issue as well. Use an alignment stick (or another club if you don't have alignment sticks) and place on the instep (just inside) your leading foot - left foot for right-handers, right foot for left-handers - perpendicular to your target line with the butt end of the club pointing toward your golf ball. Place the golf ball in-line (or within close proximity) to the shaft. Just like dotting an "i". This is where your ball position should be for today's drivers.

Striking the ball low on the face will introduce more spin, whereas striking the ball high on the face will reduce it.

Finally, depending on all of these other factors, you may not be using the right amount of loft. I haven't read much on the subject recently, but I'm pretty sure that higher lofts are better suited for players with slower swing speeds - unless of course you're using a driver with a low and forward CG like the TM SLDR, R15, etc., etc....

Hope this all helps. At the end of the day though, your best bet is to go see a certified PGA instructor for a lesson and have them assess what's happening.