First of all, congratulations on finding Jesus!!! The angels are jumping for joy for you....seriously! Welcome to a new world of excitement, danger, and often...mass confusion.
The word "Saved" is often a misinterpreted thing. We are not really saved "from" anything. Saved from hell, damnation, sin, etc... Instead, a more accurate way to look at it would be that we are saved to Jesus. All people deserve to die and go to hell...that's the nature of sin. By accepting Jesus as your Savior, you're accepting his word and allowing him to change your life. You do not actually win your ticket into heaven, you accept what has already been offered to you. If your mom accepts the invitation, she will also be in heaven. The only way that she would not get to heaven is if she did not accept the invitation by putting her earthly life in the hands of Jesus. God can use you a lot in this area to influence and challenge her as you grow. I encourage you to keep praying for her.
Look at it another way. We're all floating in the water, fresh off the Titanic. If nothing happens soon, we will either drown or freeze to death. The only way to safety is a life raft. All the rafts of the world, seemingly safe, are punctured or filled with garbage, to sink at any moment. The only raft that can truly save us is the one Jesus brings: his good news. We can choose to jump on board or try to do things ourselves, chasing after the other life rafts. But chasing after the other ones are lost causes.
The world believes that the way to eternal life is by being good and doing good things...chasing after the life rafts that are deceptively safe. But it all leads to the bottom of the ocean. Only Jesus can rescue us from that fate. Call it "original sin" or whatever the Christianese word is for it, but we are doomed from the start. Jesus saves us, pulls us aboard to him, and alters our dark destiny.