These back pains you are having along with the urge to vomit do sound concerning. The list of things that could be causing this is long. My first thought is that you may be having a problem with your gall bladder. Gall bladder pain causes right sided abdominal pain, but it often radiates to the back and causes nausea. Likewise pain that is coming from the pancreas also can cause right sided abdominal pain that radiates to the back. While gall bladder stones are more common in patients older than you, it is still possible. Your back pain could be due to a kidney stone. Kidney stones
can cause back or flank pain that radiates into the groin. This too can cause nausea. While you are correct that ibuprofen can damage kidney's, this would not cause pain, and the damage that the medicine causes usually takes years to develop.
I suggest that you schedule an appointment with your primary care physician
. He or she can take a more detailed history of your symptoms, inventory what you have been eating and what medications you have been taking, and perform a thorough physical exam. You will likely need some blood work including a comprehensive metabolic panel. Hopefully, you doctor
will be able to get to the bottom of this.