Can you show a pic of your relationships if you created them? I'm not convinced it is all wrong but that's only because I'm thinking your explanation might only relate to the structure of a form plus I have no idea what a "sheet" is in this case. Maybe it's a table with lookup fields, and that would be a different kettle of fish.
A direct answer might be: try
=sum([Diagnosis]="Anxiety")+Sum([Diagnosis 2]="Anxiety")+Sum([Diagnosis 3]="Anxiety")+Sum([Diagnosis 4]="Anxiety")
but that's a wild guess because of not knowing about the design.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.