The answer is certainly YES -- smoking can have serious and harmful effects on your kidneys. That being said, what you are experiencing is unlikely to be related your smoking. While it is always advisable to quit smoking, your current symptoms are likely unrelated to the smoking.
Kidneys are the organs that filter the blood and remove waste (in the form of urine). As they must filter the blood, there are many large vessels that feed the kidneys. One of the major problems with smoking (and there are many) is that they cause blockage formation in the blood vessels. This means the kidneys do not get the appropriate blood flow -- which means they become injured and cannot filter the blood.
Normally this process described above -- known as chronic kidney disease
-- is not painful. The kidneys can cause back pain when over expanded or inflamed (as in a kidney infection) but this is not caused by smoking.
It sounds like your back pain may be from the muscles of the back. These are large muscle that support the body. They often carry a lot of "stress" and therefore can cause some pain when in a stressful experience.
Talk to your doctor
for more information. There are treatments for back pain and investigations that can be done on your kidneys. Good luck!