My wrist had an element of stiffness for a while in the early days which was MS related so it can happen.
Arthritis comes with a lot more pain, even with small movements.
The more common symptom involves nerves going down the arm to the fingers. There are 2 separate nerves, one going to your little and ring fingers and the other to your index and middle fingers. When it's a MS nerve issue you'll have sensation issues in 2 fingers at a time.
You're unlikely to have arthritis unless you've previously injured yourself in the area you're taking about.

Ask your Doctor about the arthritis it’s the only way to tell I got both arthritis and MS so they both suck

You need an EMG test for carpal tunnel. It is Peripheral Nerve damage. Doesn't matter the cause but see a hand specialist as list for treatment
I had surgery...not a complete cure but better. I tried PT before and hand splints.

Thanks for response.

If it's MS related- it's probably having to do with the nerves or the widespread inflammation that MS causes.