Hi there and thank you for your question!
Fructose is a type of sugar that can be found naturally in fruits and vegetables but can also be found in added sugars such as sucrose (table sugar), agave nectar, honey, and high fructose corn syrup. Sucralose (Splenda) does not contain any fructose.
The most common sources of fructose in the American diet are sweetened beverages (like sodas, sports drinks, & frappuccinos) and baked goods (like pastries, cookies, & cakes).1
It may be helpful for you to speak to your liver doctor and ask them to clarify their recommendations. The doctor can also refer you to a registered dietitian nutritionist, who can assist with identifying appropriate foods for you. You can look through eatfresh.org recipes together and filter them based on your needs and dietary preferences, such as low added sugar.
Hope this helps!
Bailey, Regan L et al. “Sources of Added Sugars in Young Children, Adolescents, and Adults with Low and High Intakes of Added Sugars.” Nutrients vol. 10,1 102. 17 Jan. 2018, doi:10.3390/nu10010102