Answer
Yes. The brain can literally cause any physical sensation in any part of the body. In fact, I've had each of those specific manifestations of TMS myself. At one point had the eye twitchies. This is like a mini spasm and is often a physical manifestation of anxiety. I had tingling down my leg, which I feared was a compressed disc, but once again was TMS.
These are just two of many possible manifestations of TMS such as: dull pain, sharp pain, shooting pain, burning, chills, fatigue, itching, numbness, and weakness.
It should be stated that just because the brain can cause all of these symptoms, it doesn't mean that there isn't a possible structural cause. Once I had shooting wrist pain, assumed it was TMS, kept using it, and my palm swelled up like a grapefruit. I'd torn a ligament.
So it's always important to get structural causes ruled out. Assuming you've been cleared or the findings are relatively incidental, it's safe to assume it's TMS and once you stop engaging with the fear associated with the symptom you undermine its purpose and it begins to fade.
AG
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