My baby won't stop crying

I am a first time mom. My daughter is 6 months old and began teething, two cute little teeth at the bottom of her mouth, and of course she is crying way more than she used to. She has been pretty well-behaved so far? She didn't use to cry much before except when she was hungry/had a dirty diaper/sleepy. Now it's like she has become a completely different baby, she won't stop crying and it has been very hard trying to calm her down. I give her frozen toys, I use a special numbing gel on her mouth, I try my best to keep her well fed all the time and make sure she is clean, but if feels useless, even if I do all that it will take at least and hour for her to calm down, and when I leave the room she will cry even harder. This is not the case with my partner, they can take care of her and she won't even cry, I don't know what I'm doing wrong I feel like I suck at this, I'm scared that even though I'm trying my best it could not be enough for her. I've read that this means she sees me as a protective figure so she expresses her emotions and needs with me, and though I know this is irrational, I feel like she hates me. It's so dumb, and I'm aware. How can a baby hate? I just can't shake the feeling I'm failing at something, I don't know. I'm very sad.