AW hun she sounds just like my DS was at that age (and for the next few weeks). I found it really hard to tell what was going on with DS and whether he was hungry or wanted comfort from the pain and tbh I don't think I ever really worked it out.

We ended up with a dummy quite early with DS because he just seemed to want to suck all the time and at times that seemed to help but I remember still being confused at times about what was going on. I'm not suggesting you introduce a dummy btw just saying I know how hard it can be to work it out.

I would keep offering milk until you are sure she is no longer hungry. This won't last for long and you'll get to know each other and her feeding will settle down. Maybe try burping her more frequently during a feed but not over your shoulder but kind of in the lower tummy over your knee or arm itms?