What could be the cause of frequent urination and back pains?

Possible UTI. I would like you to be checked for a bladder or kidney infection as soon as possible. Your doctor should be able to perform a urine test in clinic, or if you have fever or vomiting, you may need to be seen in the emergency room.
Urinary infection. In a woman your age the most likely diagnosis would be urinary tract infection. You should see your doctor who will likely ask for a urine sample. Be prepared when you go to the office to give a good sample.
Urinary infection. Commonly this could be a urinary infection possibly becoming a kidney infection. These need immediate evaluation and treatment.