If family history of good health but high cholesterol, is there some genetic test I should get if mine is now high also?

No - Need Evaluation. Cardiovascular (cvd) risk is related to the number of LDL particles (ldl-p) and the number of HDL particles (hdl-p). Because cholesterol in LDL and HDL particles is highly variable LDL cholesterol (ldl-c) levels often disagree with ldl-p levels. When ldl-c and ldl-p disagree cvd risk tracks with ldl-p, not ldl-c. I recommend seeing your provider or a lipidologist to check ldl-p and hdl-p levels.
No. The fact that you have a family history of high cholesterol and a high cholesterol value yourself indicates you have a genetic predisposition for high cholesterol. Consult with your primary care physician or cardiologist to determine an appropriate approach to reducing your high cholesterol.
Yes :Apolipoprotein. I would recommend checking 2 things: Apolipoprotein E and insulin resistance measure. Inflammatory markers like C reactive protein ad Lp-PLa do help to determine the true risk for cardiovascular and neurologial issues in thelater ages like ischemic or vascular dementia. The body is making cholesterol for a reason, find out why?