Hi. I'm online and happy to answer your question today.
You are correct. That tissue is called conjunctiva and under that is another layer called tenons capsule, then the sclera, which is the wall of your eyeball.
When your eye is irritated from various things, like allergies, infection etc, the conjunctiva can swell -- this is called chemosis -- and get the crinkles that you are seeing. This is nothing to be worried about.
Does this make sense to you?
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