I noticed a single red dot on my penis near the head and didn't think anything of it because the doctor said it was an insect bite. This dot never burns, itches or anything, It has reduced in size and is not as red anymore. But the problem is it has been about two months, and it's still there. What could it be? It's one dot, not multiple, and there's no white on it, it's just red.
There isn't enough for me to go on. Remember, I can't see what you see. I assume it is small, though you didn't say how large it is. I also assume there was no bump before or currently. That it never itched is odd for an insect bite, but it would not be unusual for an insect bite mark to last a long while. Sometimes damage is done just under the surface of the skin, which allows blood to pool (small as it might be) and that is the dot that you see. The same thing can happen if you rubbed yourself too roughly while masturbating, or pinched yourself while zipping up your pants. You can also get a spot from a small infection that healed, but left behind a spot of damage that is taking longer to repair.
The fact that it is fading is the important thing. It means it is healing, even if it is going away slowly.