Did you find the locations of the punctures on the tubes? That can tell you a lot. If the puncture is on the inside or outside of the tube, that'll tell you whether your problem is inside the rim or something coming through the tire. Or it might not even be a puncture, per se-- I got a couple of flats when I first learned how to change tires. Each of them was due to a tear along the valve stem. I finally figured out that I was tightening the valve nut too tight.