Hi 2plus2plus1
You sound like you are doing really well so far! Your DD feeds well, and is gaining weight. Brilliant!
When DS was this age he had one major growth spurt a week, until he was 8 weeks old. I literally could not move from the bed / sofa for a good 12 hours while he fed, napped, woke, I changed him, and we started over again!
It's how your milk supply gets established and perfectly normal, but don;t worry, once you get past 8 weeks or so it should slow down.
I think it is normal for you to be experience days when you feel overfull and days when you feel more "floppy" while your supply evens out to meet your DD's needs!
DS only ever fed off one side as he was very sicky and would throw up as soon as he came off the breast so I never offered him the otehr side, unless, like you describe, he seemed to be looking for more. I think as you say, if she comes off and you still appear to have lots of milk, then trying her back on again for a bit longer sounds fine, if she wants it. Perhaps she gets cross because she has to work harder when your let down is slower? (perhaps a BF counsellor could advise on this?).
There were however odd times when DS fed from Boob 1, then Boob 2, then back to Boob 1 again! I think it's not a case of there "being milk there" it's a question of them needing to suckle to increase your supply.
So putting her to the breast, even when you feel like your supply is low, is fulfilling that purpose.
When you say she is screaming for milk that isn;t there, what happens? Do you put her to the breast and she comes off and screams?