It is unlikely that the chicken pox altered your daughter's food preferences, but I can understand why you might think it did. Between 8 and 10 months, babies start to make simple choices about what they do and don't want. She is actually eating quite a variety for a 15-month-old. But to get her to eat an even bigger variety, you're going to have to make some changes.
To start, she should drink only from a cup. Bottles should be stopped when your child begins table foods. Also, mixing half and half with whole milk is giving her a very high-calorie beverage; that alone is most likely keeping her from ever getting very hungry. At her age, I would recommend no more than four 4-ounce cups of whole milk only for her milk intake.
If her cravings for nuggets and fries are frequent, you should consider avoiding the burger place and give her baked chicken strips cut into non-choke sizes. Make home-made baked fries by cutting potatoes, spraying them with cooking spray and baking them until soft. Cereal is a great food for this age. If the peanut butter is on the toast, she has a great protein source there.
At her age, your daughter's becoming more independent and curious. She will be more likely to try anything she can pick up herself. As for dumping her food, it's often a game little kids play to get a reaction. When she does this, take her out of her chair and let her go on her way. She is either telling you she's not hungry, or she will soon realize this activity will not get her the anticipated results and she'll stop.
Finally, stop worrying! She's not growing as fast as she was a few months ago, and doesn't need as many calories. Please take a look at our article on feeding toddlers to get some more ideas. You are being a great Mom just by being concerned, but your daughter is more normal than you realize!
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.