Whenever I pet my cats back theres always dandruff towards her lower back. Also, my hands get really sticky after petting her. Why is this? Is this normal?
It sounds like she is unable to clean herself properly because of her weight. Visit your vet to get advice on what to feed her, and how much. Engage her in regular play sessions so she will get some exercise.
Until she loses the weight, you will have to help her clean herself. This video will show you how to do a "mini-bath" with a damp, slightly soapy cloth.
I am surprised that at just 3 years old she is so overweight that she can't clean herself. When you visit the vet, he or she can check that there isn't some other health problem (e.g., back pain) that is making it difficult for her to clean near her tail.
As a previous owner of a cat with the same problem who was not too overweight to clean himself, I would guess that genetics (breed) has something to do with it. Certain breeds have more oily/dryer skin than others which require more attention to their grooming care.
You should still visit your vet to help determine the cause, or at least the implications (i.e. Does the dandruff mean she scratches herself too much, implying fleas etc. Determine if the stickiness means she has access to something that gets on her fur such as piping, plants, something outdoors, or is the stickiness produced by herself).
Of course if she is overweight, then self-grooming is likely a cause. Just wanted to give another POV.