15 month old throwing tantrums

My 15 month old has recently gotten into the habit of throwing a fit about everything. She has learned how to completely fall backward and fall all over the floor if she doesn't get her way. And if I'm holding her she crawls up my body and tries to fall backwards. I will admit sometimes I do spank her because shouting doesn't work and it's overwhelming sometimes. Yes I do shout quiet aggressively because no matter how nicely or how many times I tell her not to do something she completely disregards me and does it anyways again and again. I try to be patient but everytime I do something she doesn't like or she doesn't get her way she just screams until she gets her way. The whole day I'm trying to balance housework, my screaming child hanging in me as I'm cooking and cleaning and balancing family health issues and I start work next week. Please do not judge me. I feel as if though I may not be giving her enough time or playing with her enough. I've tried researching gentle parenting. I've tried talking it out, saying it's ok to cry but she's fights me so hard. I feel like I'm failing her as a parent. I don't know what to do.