antinuclear antibody (ANA) with reflex panel (done if ANA is positive to get more specific info)

Sed rate, CRP
As the parent of a type 1, I would also say you need more aggressive help with blood sugars. Insulin needs to be tripled sometimes in our experience with infection, and with steroids like Florinef. It is concerning that you had ketoacidosis with a throat infection. Were you on steroids?

Are you on insulin? Diabetes is certainly a low hanging fruit here so to speak. If blood sugars are under control a lot changes. Can you do a pump and CGM?