My rabbit is shaking her head and scratching a hot ear. What's wrong?

I am sorry to hear that Paisley isn’t feeling well, and thank you for your question. From what you are describing, she could have an ear infection. Unfortunately this is very common in lop eared rabbits, and often gets quite severe before they show any clinical signs at home. It may also be affecting both ears, and she may not be showing it. Ear infections can be simple and only affect the external ear, or they can be deep and be present past the ear drum and into the middle and inner ear.
My recommendation would be to take Paisley to a veterinarian who is familiar with rabbits. They can perform an exam of the ears and collect samples to look for infection. They can then prescribe anti-inflammatory pain relievers and may prescribe antibiotics as well. If they suspect that the infection may be deep, they would recommend imaging with radiographs (x-rays) or a CT scan. Please don’t give Paisley any human medications, as many of them are harmful to our furry friends.
I would not recommend cleaning the ears until you have visited the vet either, as many cleaners are not safe to use if you don’t know if the ear drum is intact or not (i.e. they can be damaging/toxic to the middle and inner ear).
I hope that gives you a place to start, and I wish you and Paisley the best of luck!