Children often have very different ways of learning, and of accomplishing certain skills. I'm sure you've tried talking with your daughter.
Now may be a good time to try a different way of teaching her the important character traits of modesty, generosity, and kindness.
Try role playing, and playing a game called "Listening". Find a simple, subtle code word or action (tapping on your ear lobe, or putting your finger to your lips, or raising one finger. Make it fun. When your daughter sees or hears that code, she listens, without speaking. It's important that she doesn't just tune out, but that she can repeat what was said to her brother ("he is getting tall" or "he knows how to count to 6!"). Practice. Have another adult make a comment, and you give the code, and your daughter has to listen in silence. Then have the adult talk to your daughter. Ask her something specific, like "what is your favorite part of dance class" or "tell me about your teacher" etc. And while your daughter replies, you listen carefully and attentively, demonstrating careful and respectful listening. After awhile, with practice, your daughter won't need the code. She'll have developed the ability to listen and to share appropriately.
By all means, don't ever praise a child exclusively in private - that won't ever happen in school, at a job, in college, in life. People get recognized in public for their accomplishments, and often not everyone gets the same award or recognition. It's valuable to learn to celebrate with the person, to not resent them, to know how to properly acknowledge an achievement that someone else has attained.
Many kids need a visual cue or audible cue to learn a skill that doesn't seem to come naturally to them. My son, when he was in elementary school, had a habit of humming to himself when he was working in class. He didn't do it to be rude, he wasn't even aware that he was doing it. The teacher tried all kinds of things to get him to stop humming out loud. Finally, she wrote "silence" on an index card. When he started humming, she'd simply place the card on his desk, without saying a word to him. That visual cue was all he needed to remember to stop humming.