Do these show up when there’s a background check on me and how can I get them taken off of my record since I was not convicted?

I was detained for 6 days in jail for HD11379 transp/sell but I received a DA reject. It shows disposition result unknown and then I was detained on a PC 459 burglary and I also didn’t do anything. I was with someone who got caught stealing but I didn't steal. However, I got arrested with the girl that did it. Disp code was insufficient evidence but only on mine. I was released with nothing further to ever come of these cases. Why should I be punished indefinitely so I can't get a regular job and I can’t. I thought felonies were the bad ugly job stoppers not something that I didn't do. Can you shed some light on how I can fix this, please?