If she checks out as negative for an infection, possibility number 2 is for some reason, some cats decide at some point in their life that one toilet isn't enough for them. They want one box to urinate in and another to deficate in. Add a second box to the household and see if that solves the problem. Also, in the new box, use a litter called Cat Attract. It is fantastic at helping with problems like this.
Lastly, cats react strongly to stress - and usually inappropriately. If there are changes in the household, this may be her way of dealing with them. Even minor things you don't think of like more activity, guests, remodeling - they are all confusing to a cat and that can trigger this behavior also. Since you've recently moved-this is a huge stress factor for her. The stress can also cause the shedding you are seeing. Putting feliway plugins around the house can help soothe them during periods of stress, and may take care of the problem all together. They are odorless to humans, but put out phermones that are calming to cats. You can get them at most pet supply stores, or online also.
Since your girl is spayed, the issue is definitely not hormonal. If the shedding doesn't stop in a month or so, once she's had a chance to get used to the new place, you can add a product called Shed Stop or Shed X to her diet. That will help. Extra brushing and grooming will also help with that. I think if you go through the check list above, you'll hit on the answer and stop the behavior before it gets any worse. You need to make certain you clean any areas she has used to urinate on with an enzymatic cleaner that will break down the urine and remove the smell totally. Natures Miracle and Zero Odor are 2 products that will do this. If the urine is not removed, she probably won't stop going back to those places.
Canine Health Care & Guidance
Qualified by many years of healthcare & experience in breeding dogs