If the doctor has not prescribed you with an antibiotic, he is clearly wanting to get the results from the laboratory to identify the bacteria so that he will be able to prescribe the correct antibiotic to treat the infection.
You don't always get symptoms of discomfort with urination.
The painful lower back is probably because of the infection.
Sometimes we can just get bacteria that causes the infection, sometimes it may be kidney stones.
Make sure that you wipe your bottom from front to back to avoid getting any bacteria enter your urethra. And drink plenty of fluids, especially water. 2 litres of water a day is usually recommended, more if you sweat a lot. Your doctor or urologist may advise you drink more, so follower their advice.
When you have any urinary infection - it is very important to drink the fluids as mentioned above.