It could be that you're inserting it too far or not far enough, causing discomfort. Try it as far as it will go - comfortably. Experiment with different brands and absorbencies as well. Using a tampon with too high absorbency for the flow will cause discomfort, especially upon removal. A teen "slender" brand may work for you and one with an applicator may be easier to use. A type for a lighter flow may be easier to try at first. If you still have difficulties, you could talk to your doctor or nurse about it.
Diving without any protection would probably not be recommended. It sounds like your flow might be extremely light if you would consider not using anything. In that case, you could use a pantyliner or thin pad and change it between dives if possible as it will be water-logged but it will protect your clothes. If you need clothing protection on land, you will need something for your dive day as well.