Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with a doctor.
Without the ability to examine and obtain a history, I can not tell you what the exact cause of the symptoms is. However I will try to provide you with some useful information.
The description you provide does seem most consistent with a median nerve entrapment. Bilateral carpal tunnel syndrome is not uncommon. Neuropathic pain can be a tingling sensation, numbness, itch, etc. I agree that you should see a physician regarding your symptoms. You will likely need to see a neurologist. You should have an EMG/NCS test performed to evaluate the nerves and likely etiology of your symptoms. I doubt the muscle spasm is the cause of the bilateral symptoms, but you may also benefit from an MRI of the cervical spine since you do have bilateral symptoms to rule out disc herniation, etc.
In the meantime, you may benefit from a wrist splint that can be purchased from your local pharmacy.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck with your appointment. Keep us updated!
Thank you very much again for your advice, Dr. Newey. I'll keep you posted. :)