The leaf scars are very close together and the stem is thinner where they appear as if I had wrapped something around it. It also looks like it has stretch marks. Is it due to my watering or bugs? Thank you.

It had some slow growth at that point, might have been an extreme dry spell or they were rootbound. It's nothing to worry about at this stage.

Did all the rain we've had cause this problem? I've never seen my plumeria do this flop-over thing...

That is probably from the heavy rains. Other reasons could be root rot.

However, For as long as the base is not flooded or soaking with water (meaning it drains after the heavy rain) I don't hink you have to worry about a root rot.

You could cut off some of the heavier leaves.