She will definitely get benefit from it - any breastmilk is good!
Firstly, if you got sore in hospital, can you get your midwife to check your latch? I'm no expert, but remember to aim up towards the roof of her mouth, and get lots of the areola under your nipple in. If she only has nipple it hurts! Also, put Lansinoh on after every feed.
The issue with mixed feeding is that you may not stimulate your supply enough to continue feeding as long as you want to. Your supply will literally dry up if she doesn't stimulate it regularly ie every few hours.
I would try her at the breast every time she feeds and top up with formula if required. Don't get obsessed with the numbers game - it doesn't matter how many ounces she takes from a bottle, if you can hear her swallowing breastmilk you have to trust she's getting enough. This can feel like a leap of faith so look out for wet and dirty nappies as they are a great sign baby is taking enough milk.
Also, time at the breast is not a great indicator of how much they've taken.
My DD latched at skin to skin, but then was cup/tube/bottle fed for the first 6 days. Since then we've been exclusively breastfeeding - a less than perfect start is not a barrier to successful feeding! DD is now 6 weeks and thriving.
I'm completely rambling now ... These night feeds are tiring!
Congratulations and good luck.