I am an unfit mother!

I cannot say this to anyone around me so I’m going to say it here…. I have a 3 month old crappy napper and it feels like all my energy goes in making her sleep/nap. She barely sleeps during the day. And after she wakes up she’s usually too tired to play and do anything. So she’s always grumpy. All this hard work I put in is worth it if I get a 10 second smile but all I get is purple crying and breaking my back rocking her. I don’t do contact naps because I’m really trying to sleep train her (I know she’s too young but I’m scared that once she gets used to it she will never leave me alone. What kind of a mother wants to be left alone? The only free time I get is the few hours at night when she sleeps. And that’s when I sleep too…….. Everyone says newborn phase is hard but she’s beyond that. Shouldn’t it be easier now? How will her brain develop if she won’t sleep? I’m just so done. My husband helps a lot and that’s all the help I have. Sometimes I just want to run away or disappear but I cannot leave my poor baby behind. I do love her and I wait for that 10 second smile to make it all worth it.