Trying to rebuild credit

So my situation is bad but I feel like it’s fixable.I made a lot of bad decisions when I was 18(I’m 21 now) and it’s biting me in my ass. In total I have about 13k in credit card debt with a utilization of 93% and I’m sitting at 556. I have a lot of late payment’s but I’m trying to clean everything up. If I lower my utilization to around 30% will my score jump up ? Also is there a way I can remove those past late payment’s? I’ll appreciate any advice. Thanks