How can I achieve my goals if my past mistakes makes me negative and aren't letting me do things?
It doesn’t matter. We all make mistakes, some of us bigger than others. Does not matter if you were incarcerated, damaged your family relationships, were a drug addict/alcoholic, believe you ruined lives, or just feel like maybe you should have done better in school so you could go to college.
The past is the past, there is nothing you can do about it.
If I felt this way, I would engage several techniques to lessen the emotional impact that these thoughts and ideas have on me. You can probably Google some ways to change your mindset.
There are so many rooted in NLP, positive psychology, energy work, meditation, mindfulness and more.
I would just engage one technique for a month and if that doesn't feel like the technique lowered the emotional impact, move on to another one.
I would measure and track my progress. So before I started working on it, I would scale it on a 1 to 10 scale (10 being massively intense and feel like the statement is very true) then at the end of the month, scale it again.
But here is the bigger thing. The way in which you phrased your question, shows me that you are in a state of blame and believing that something outside of you is preventing you from doing things. I refer to this as having a victim mindset.
Now, this could be true, Like you were incarcerated and now you are unable to vote, somethings are factual, but they in no way prevent you from helping a person get elected. But if you are stuck seeing how the system is holding you down and you can simply vote, you are still stuck in a mindset that holds you back.
Nothing, isn't, "letting" you do things. You can move on even if the people around you can't.