What is sugar alcohol and can it affect my blood sugars at all?

Yes: Alcohol is a carbohydrate and will raise your blood sugar.

Sugar alcohols: The funny thing about sugar alcohols is that they reconstitute into actual sugar once digested. So a product can be marketed as "sugar-free" if it contains sugar alcohols, but after absorption there's sugar again. It's a marketing ploy. So yes, sugar alcohols can have bad effects on your body just like sugar.