They could cause your back to hurt, especially if the pain is localized to the area of the ovary and is just radiating through. I don't think they would have anything to do with burning when going to the loo, though. If anything were to be draining from a cyst, it would probably find its way out through the tubes, uterus and vagina rather than the urinary tract.
I agree with the previous poster. Hope you feel better soon. :)
Your story sounds semi-similar to mine. I was having some severe lower back pain, and I felt like I had a UTI and I ended up having to go to urgent care and was treated for a UTI. A week later I was still in massive pain that was radiating to my pelvis and my legs. I had blood work, urine cultures, an ultra sound, t/v us, and a CT scan and it showed I had a dermoid on my ovary. The whole time I had blood in my urine and ended up passing three kidney stones.
I know there isn't any real advice in there, but I felt very similar to you so at least you aren't alone. I don't know if the size of your cyst can lead to that much pain. I think it all depends on where it is. I believe it is possible for it to push against your bladder or bowels causing pressure. My dermoid is 2.0x2.3cm as of my last ultra sound, and I know it causes me some pressure and discomfort.
Best of luck to you!
Thanks to you all and good luck to you too. I am sure there is a pill to fix me haha. I am sure the dr. will fill me in on what to expect, I will be glad when it is all said and done.