Have you tried giving her gas drops? I find the little tummies gas drops work wonders on my LO.
For burping, try different positions if you're having a difficult time getting a burp out. Over the shoulder, sitting on your thigh- support her chest with one hand and place them and fingers around her jaw/chin to support her head. In this position you can also slowly rotate her in circles your tip her backwards and forwards slowly (if it scares her, don't do it). Another way is to lay her tummy down across your thighs. I find these techniques are really helpful for getting out stubborn burps.