No your milk won't technically come in like it would have the first couple of days, but you might find yourself 'xtra full' now. It shouldn't be painful, it just is a more full feeling.
As long as you are producing some milk, in a few days you will produce enough milk.
From a physiological standpoint you are past the time when your body makes milk automatically. You have prolactin receptors 'turned on' in your breast. The more that is turned on, the more efficient your breasts are at making milk. (More receptors = more empty que = more milk = seemingly faster milk production).
In MY experience, if I wanted to get my production rolling strong, you need to absolutely EMPTY a breast. Like it almost feels flat it's so empty. A breast produces based on emptiness (the number of open prolactin receptors). If you want your breast to realize it needs to make more milk, you need to empty it completely. Also, milk fats accumulate on the walls of the ducts and little storage sacs. Make sure you are massaging your breast as she eats so that those fats are released, and your breast empties even further. I wouldn't worry about offering both breasts,
unless she is that hungry. It'll take a couple of hours for your breast to fill after being emptied, but know that you are continuously making milk. If your baby was hungry, she could continue to suck and get some milk.
This is what I do: I offer one breast. She'll empty it 90% of the time. If she doesn't empty it for some reason (just wanted a quick drink before her nap or needed some comfort sucking, or close time to mama) if it isn't very long before she wants the breast again after that, I'll put her back on the same breast to eat and empty. Then move to the other. The idea is to try to make empty breasts. Not only is that baby getting all the fats (yum) and getting more satisfied feeling (takes longer to digest fats), she is making your breasts know what she needs as far as amounts.
Your breasts might go into a bit of overproduction doing this (they may not though). You can decide what to do with the overproduction... you can pump it for storage, or just pump a little off to be comfortable and let your body regulate down to her specific needs.
I hope that helps answer some of your questions. Though it sounds like you are doing fabulously!