Welcome! My name is***** am a UC Davis graduate, and currently, a Medical Director of a veterinary hospital.
I am sorry to hear about this concern for Emily.
Well, a few concerns.
You are describing several issues with the bladder:
1. inappropriate urination
3. keeps licking
This could suggest a urinary tract infection, bladder stones, and I can't say there isn't something else in the bladder like a tumor. So, the bladder symptoms are serious.
Drinking more water could be a symptom of a urinary tract infection. But, other conditions that could cause increased water intake (polydipsia) are kidney disease, diabetes
or Cushing's disease. Cushing's, is when the body is producing excessive amounts of its own steroids.
Then, she is also having diarrhea. So, without question, Emily needs to get in to a vet and without delay. In addition, we have no way to tend to these symptoms with at home care. Very sorry that Emily is not feeling well.
I would suspect the vet would recommend a basic blood and urine test to start, as well as, some supportive medication for the bladder.