What to do if I don't want to go on cholesterol meds. If I stop eating for a week will my triglycerides go down?

Probably. The triglycerides are much more labile than the cholesterol and do go up substantially after eating. You need a low carbohydrate diet. I doubt if many doctors would recommend fasting for a week but you need to reduce the portions of food, cut out the in between meals eating, and restrict carbohydrates. The triglycerides are much more responsive to life style changes than the cholesterol.
Probably but only .. They will but they will go up again once you start eating again.