Is "functional sensory symptoms" or "functional sensory syndrome" a real thing? I get weakness and tingling on one side frequently. Not a stroke.

Other causes. Transient neurological symptoms (such as weakness, tingling) can happen for various reasons. We always try to rule out "bad" causes first - strokes, seizures. Often times times migraines can cause them. At times patients get them when they are stressed or anxious (panic attacks etc). "functional" here means no "structural" cause was found. Few of my patients benefited greatly from meditation.
For any condition. That is "functional" to the patient, the symptoms are real and not feigned, the brain is playing tricks on your body. Getting patients to accept a diagnosis is not easy. I advised that you research if there are any behavioral health groups in your region that are experienced with these conditions. Again, you are not crazy, but you do need to seek assistance.