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.
de Quervain's tenosynovitis is inflammation of the tendon of two of the muscles in the wrist. It is classically described in patients with repetitive use (e.g., sewing, golfing, fly fishing, etc). The symptoms vary but patients may complain of pain in the wrist on the outer side particularly with grasping and thumb extension. The Finkelstein test, as you mentioned, is performed by grasping the thumb and then abducting the hand (e.g., like in casting a fishing line). Pain with this is a positive test result. The diagnosis of this condition is clinical, meaning that the physical examination is very important as well as the history taking. Many physicians will get an xray of the wrist to rule out other conditions. The treatment of this condition involves NSAIDs, ice, spica splint of the thumb, and local injection of anesthetics or steroids. If conservative measures fail, surgery may be an option, but success rates vary.
I am unable to view the video link you posted. However, differential diagnosis of de Quervain's tenosynovitis includes arthritis, but also carpal tunnel syndrome, and cervical radiculopathy to name a few. Pain at the outer elbow may be tennis elbow (or lateral epicondylitis) which is another “overuse” joint condition. Muscle spasm has a very broad differential ranging from benign fasciculation syndrome to viral infection to anxiety to seizure to ALS. It is always of use to have basic laboratory work, including thyroid panel, complete metabolic panel, magnesium, calcium, and complete blood count, checked to rule out other potential causes of muscle spasm.
I recommend that you continue working with your physician on this diagnosis. You may need a referral to a neurologist if a diagnosis is unsure. De Quervain’s tenosynovitis is a clinical diagnosis as well as many of the differentials of this condition.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.