I second getting checked for tongue tie, as soon as possible. Also, painkillers! I used the ones I was discharged with from hospital, and got a repeat prescription for them from my GP.
Nipple shields may help in the short term, especially to allow healing, but also try lanisoh.
You should get your latch checked, just in case, but please do find someone experienced with tongue tie to check your baby, as misshapen nipples, nipple trauma etc are all symptoms.
DS1 was tongue-tied, and still gained weight beautifully (his tie was snipped at 11 weeks) It's a myth that tongue-tied babies struggle to gain weight. The pain, however, was awful. When DS2 was born, it was the first thing I wanted him checked for.
When you look at your baby's tongue, can you see a tie? Is her tongue notched at the end when she sticks it out? Can she stick her tongue out past her lips (try doing it yourself, and seeing if she will copy). Even if you little girl doesn't have any of these visible signs, it doesn't mean that she definitely doesn't have a tongue tie. DS1 and DS2 both had posterior tongue ties, which could only be diagnosed by touch (and by my own symptoms).
If your little girl is tongue tied, positions that use gravity to help her tongue fall forward may help a little. I also ended up expressing 1 feed a day to give myself chance to heal. Once DS1 had his tie snipped, I went back to feeding him myself.
If you post the area of the country that you are in, someone may be able to suggest a person exerienced in tongue ties to help you. Alternatively, you could look for a lactation consultant with experience in the area.
There is also La Leche League, who have a helpline and can also give advice by email. I found them helpful.
Please don't just struggle on - there is help out there. It really is fantastic that your little girl is thriving, but your pain is important too.