I have a flat tag on the side of my penis for 6+ years. Looks exactly like a wart would look. About 2mm wide. It has never changed, never got bigger, and no other spots have popped up. Wife never got any warts either. I have read other forums where people have had wart-like flat tags. So, don't worry. It's almost certainly not an STD.
They aren't genital warts if you've had them since 2002. HPV would have cleared your system by now.
They could be skin tags, dematofibroma, or really, a host of other things that are totally normal, but to find out for sure, your doctor would have to take a look and perhaps biopsy them. There are lots of things that cause bumps on the penis, and many look alike, so testing is the only way to know for sure.