Error in law (wrong criteria)?

If you think the tribunal probably got the law wrong then definitely appeal, especially if the evidence suggests the decision might have gone the other way had the law been properly understood. Here’s a case where the Upper Tribunal found an error of law in similar circumstances: M v An NHS Trust [2017] MHLO 39 (UT). Reading the case it looks like the patient there had a flimsier case than yours.