Yes cats can get Urinary Tract infections, among other things that can cause her to go outside the box. The infection is painful and they often associate the pain with the box so they look for a place to go that isn't painful. The fact that she's holding her urine suggests she is trying to avoid peeing which suggests a UTI. If that's the cause, antibiotics will quickly clear it up. She must be seen by a Vet, ASAP. You can also check this thread on peeing problems: http://www.thecatsite.com/forums/showthread.php?t=9563
You can also collect a spoonful of uring and take it to your vet for analysis.
Don't delay in getting this taken care of.