I'm changing my first inner tube after getting a puncture in the back wheel. I had to put the tube in water to find the puncture and it was a tiny hole on the inner side of the tube. On the wheel I can't see or feel anything that would have caused it. Any advice? Or do I just put a new tube on and see what happens?

Edit: Thank you all for your detailed advice. Looking at it again today I realise that it's not my finest hour - when I inflated the tube to check it out it's flipped inside out with the valve facing outwards. So the puncture was on the tyre side of it, not the wheel side. I still can't see what exactly on the tyre caused it, but at least it's less of a mystery now!