Hi K.,
FIrst of all, great job breastfeeding! You're giving your daughter an invaluable gift (and yourself -- that snuggle time is precious, isn't it?)
Please do not worry about the right vs. left breast thing. It is not actually important that a child nurse from both. I'm a training lactation consultant and I promise you that your baby is doing great if she's nursing on one side. Your one breast will accommodate her needs, no problem. There is magic that happens between a nursing mom and her baby. Your bodies communicate and adjust to each other in ways that science can't yet explain, and our brains don't even need to understand.
You're wise to hold the bottle up and capture some of that milk. It might be wise to pump afterward, as well, or during the nursing so that you have extra milk for an emergency and that breast continues to be stimulated to produce milk. Do consider using the breast horn part of the bottle when you capture the milk for minimal bacterial contamination of the milk.
My left breast let down too forcefully for my young babies to suckle at. I continued to offer it to them and they would pull away. Eventually they were able to handle the pressure of the milk flow, but not at first. Some women never are able to nurse off of one or the other side and that is FINE. Please do not worry! Just keep nursing, you're doing great!