I missed that you had her! Congrats!!! What a beauty! WTG on the nursing too - woohoo!
You can nurse either way, as far as both at a feeding or one at a feeing. In my personal experience, when they are tiny, one side at a feeding, take off burp and relatch on that side works good because they get all the good hindmilk too which can help them be less gassy.
However, it helps to have some supply going first, and keep an eye on that, making sure both sides get a workout. MY milk coming in would adjust after a bit and get fuller on one side only, and then as they got older and could do both it adjusted back.
As far as the latch, keep taking her off and relatching, using your thumb to pull down her bottom lip until she is latched on the right way. You can do alot with your fingertips, as far as shoving more nipple in there and making sure her lips are splayed out the way they are supposed to be. A wrong latch can go from sore to cracked open and bleeding REALLY fast, so give it a good go with each feeding to get it right. Once they are sore it is hard to tell if it is right or not, it just HURTS!
Also, maybe try a different hold. If she latches better laying on her left side, keep her on that side and wrap her legs around your side and back, if that makes sense. Is that the football hold maybe? It helps to be in the comfort of your own home where you can have your shirt off and manuever a newborn around!!
Again, congrats! Enjoy your babymoon!