Hey there, welcome to the boards.
It's normal for that to happen sometimes. But it sounds like the way you approached this caused you pain, so next time, you'll want to take that note from your body and stop what's causing you pain. Then you can try and find another way. My best suggestion is to take your washrag, soak it in warm water, and just use it like a compress on the hood. You may need to sit with it for a little while, and warm up the water/rag a few times. That will soften those oils so that they can just kind of melt away.
I'm sure that you haven't done any damage: that part of the clitoris in particular is where the bulk of its sensory nerve endings are, so yeah, when we hurt it, it can hurt like nobody's business. I'd just be gentle with your body for a bit, and if you have any aloe vera handy (not the kind with additives, from a plant), that is something you can put on the area to soothe the skin there.