I went on a ride about a week ago, didn't go far but just wanted to get out for a little bit while I had the time. Everything went well, no flat when I finished my ride. When I went for a ride a few days ago I found my back tire to be flat, wouldn't take any air at all. I took off the tire and changed the tube, everything seems to be fine but I haven't ridden it yet. I noticed on my old tube the hole is right at the base of the stem, and it looks like something cut the tube because there is a little flap of rubber. My question is---is it possible that there is a burr or something on the rim that could have cut the tube? Have any of you got a flat tire from the rim, but not like a pinch hole? I got the other tube on the rim before I thought to look and see if something was there. Seeing as this is my first flat replacement I'm a little hesitant to go out on a ride because I don't have a seat bag to put a tube and some tire irons in.

Thanks!