Any time you have pain, regardless of whether or not it is or is not controlled by over the counter pain medication, you should always see a doctor. In the case of low back pain, you should first have your primary care physician
Pain medicine is an important part of back pain treatment. However, even more important is figuring out what is causing the pain so it can be reversed. In terms of the medicine you are taking, there are other versions of over the counter anti-inflammatory drugs like Advil that may work better for you. Tylenol is a great drug for this pain, but often is used in doses that are insufficient to treat the pain. Prescription strength anti-inflammatory drugs can be very helpful in certain patients. Finally, in some rare instances, narcotic pain medicines can help, though there long term side effects usually make their long term use more harmful than helpful.
I suggest that you schedule an appointment with your primary care physician. He or she can listen to your description of the pain, examine your back closely, and narrow down the possible causes of your back pain. If there is any specialist that could help, then you can get a referral to that doctor. The possible referrals that could help you would be an orthopedic surgeon
(if you have a pinched nerve), a rheumatologist
(if you have an inflammatory arthritis), or a pain medicine specialist. In addition, you can ask your doctor about physical therapy which can help with the pain. I hope you feel better soon.