overfeeding?

I ebf my 7.3 week daughter. She likes to nurse till she falls asleep. At times when she's just aboutttt to fall asleep she becomes increasingly fussy at the breast by latching unlatching and wanting to latch again. As soon as she latches she unlatches and the cycle repeats. At first I thought she does it coz of lack of milk but now I can hear her gulp so I think it is because of milk. She sort of wants to nurse but not drink milk, if that makes sense? Since she's full 
She also has silent reflux and that also bothers her as such that she'd be feeding but the milk comes up to her throat and goes down and I hear that. I know I should burp her but when I try to she resists acting super hungry. I almost have to fight that burp out of her 
I don't wanna give her paci for fear that she'll suck in air plus cleanliness issues