Yes, URI can clear on it's own. It is not advisable to try to wait it out as it can quickly over come them. The only land animal in the animal kingdom that cannot manufacture their own vitamin C is the primate family. This makes use very subseptible to all viruses and bacterias. The only time other animals have to worry about something like this is when their macronutrients (sun, water, air, and earth) and primary nutrients (food) are not favorable. This makes their body struggle to supplement these things any way it can, all the while lowering their immune system and leaving them open for another problem. Intra species spreading of pathogens is possible but other animal's immune system are far more advance then are own so it is highly unlikely. If you do have a case of a clear up take a look at what the differences of the conditions before and after were. This is probably where some changes should be made to accomodate her in a better enviroment.