Thank you for your reply.
The symptoms you are describing in your left arm and hand (thumb) can definitely be caused by a pinched nerve in your neck. The same pinched nerve can cause you to have neck pain and stiffness.
Prior to getting any treatment, it is important to get a proper diagnosis otherwise treatment can actually cause some harm if no specific diagnosis has been made. There are 2 tests which can be done to evaluate which nerve is being affected and how much. One test is called EMG (Electromyography) and another one is MRI of your neck. Once you get an exact diagnosis, you can decide on the treatment plan. I am not a huge fan of acupuncture or chiropractor medicine and instead prefer physical therapy for treatment, however, acupuncture can probably compliment physical therapy.
A pinched nerve in the lower back can cause pain in lower back as well as radiation of pain into buttocks, thighs and down the leg although your symptoms are not very specific for a pinched in a lower back. However, the same EMG test can be done on the nerves coming from your lower back to see if any of them are affected. Sometimes a pinched nerve in the back can cause symptoms due to inflammation in the lower back, but often it can subside on its own. If these symptoms are relatively new and are not very bothersome to you, I would suggest you concentrate your neck issues first, try to get a proper diagnosis and treatment.
I hope you find this information helpful. Please feel free to follow-up with any other questions you might have.
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Best wishes and good luck,